diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4fa5790e..beb43563 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -14,6 +14,9 @@ CHANGELOG
       ```vim
       let g:fzf_layout = { 'popup': '90%,70%' }
       ```
+    - fzf now opens in a tmux or Zellij floating pane by default, so the window it was started from stays visible and can be used while fzf is running
+        - Requires tmux 3.7+ or Zellij 0.44+
+        - Set `g:fzf_layout` to pick a different layout
 
 0.74.3
 ------
diff --git a/README-VIM.md b/README-VIM.md
index 70c5b37a..ba505e45 100644
--- a/README-VIM.md
+++ b/README-VIM.md
@@ -1,6 +1,26 @@
 FZF Vim integration
 ===================
 
+<!-- vim-markdown-toc GFM -->
+
+* [Installation](#installation)
+* [Summary](#summary)
+* [`:FZF[!]`](#fzf)
+    * [Configuration](#configuration)
+        * [Examples](#examples)
+            * [Explanation of `g:fzf_colors`](#explanation-of-gfzf_colors)
+* [`fzf#run`](#fzfrun)
+* [`fzf#wrap`](#fzfwrap)
+    * [Global options supported by `fzf#wrap`](#global-options-supported-by-fzfwrap)
+* [Tips](#tips)
+    * [fzf inside terminal buffer](#fzf-inside-terminal-buffer)
+    * [Starting fzf in a Vim popup window](#starting-fzf-in-a-vim-popup-window)
+    * [Starting fzf in a tmux/Zellij popup window](#starting-fzf-in-a-tmuxzellij-popup-window)
+    * [Hide statusline](#hide-statusline)
+* [License](#license)
+
+<!-- vim-markdown-toc -->
+
 Installation
 ------------
 
@@ -133,19 +153,35 @@ let g:fzf_action = {
   \ 'ctrl-v': 'vsplit' }
 
 " Default fzf layout
-" - Popup window (center of the screen)
-let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
+if exists('$TMUX') || exists('$ZELLIJ')
+  " The Vim plugin will try to open fzf in a tmux or Zellij popup
+  " if possible (requires recent fzf and tmux/zellij) using --popup option,
+  " with the following argument:
+  let g:fzf_layout = { 'popup': '90%,60%' }
+else
+  " If --popup option is not available, it will open in a popup window inside
+  " Vim (center of the screen)
+  let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
+endif
 
-" - Popup window (center of the current window)
+" Here are some more layout examples:
+
+" - Tmux or Zellij popup at the bottom 40%
+let g:fzf_layout = { 'popup': 'bottom,40%' }
+
+" - Tmux or Zellij popup at the top with a different size
+let g:fzf_layout = { 'popup': 'top,90%,40%' }
+
+" - Vim popup window: at the center of the current window (relative)
 let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6, 'relative': v:true } }
 
-" - Popup window (anchored to the bottom of the current window)
+" - Vim popup window: anchored to the bottom of the current window
 let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6, 'relative': v:true, 'yoffset': 1.0 } }
 
-" - down / up / left / right
+" - Vim split window: down / up / left / right
 let g:fzf_layout = { 'down': '40%' }
 
-" - Window using a Vim command
+" - Vim window using a Vim command
 let g:fzf_layout = { 'window': 'enew' }
 let g:fzf_layout = { 'window': '-tabnew' }
 let g:fzf_layout = { 'window': '10new' }
@@ -408,10 +444,10 @@ Tips
 
 ### fzf inside terminal buffer
 
-On the latest versions of Vim and Neovim, fzf will start in a terminal buffer.
-If you find the default ANSI colors to be different, consider configuring the
-colors using `g:terminal_ansi_colors` in regular Vim or `g:terminal_color_x`
-in Neovim.
+When fzf is configured to start in a terminal buffer inside Vim or Neovim, you
+may find the default ANSI colors to be different. In that case, configure the
+colors using `g:terminal_ansi_colors` in regular Vim or `g:terminal_color_x` in
+Neovim.
 
 ```vim
 " Terminal colors for seoul256 color scheme
@@ -442,7 +478,10 @@ else
 endif
 ```
 
-### Starting fzf in a popup window
+### Starting fzf in a Vim popup window
+
+You can configure fzf to start in a Vim popup window by setting the `window` key
+in `g:fzf_layout`.
 
 ```vim
 " Required:
@@ -458,18 +497,32 @@ endif
 let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
 ```
 
-Alternatively, you can make fzf open in a popup window (requires tmux 3.3 or
-above, or Zellij 0.44 or above) by putting `--popup` option value in `popup`
-key. `tmux` is accepted as a synonym, just as `--tmux` is an alias of
-`--popup`.
+### Starting fzf in a tmux/Zellij popup window
+
+fzf can also start in a popup of the multiplexer instead of a window inside
+Vim, by putting a `--popup` option value in the `popup` key. `tmux` is
+accepted as a synonym, just as `--tmux` is an alias of `--popup`.
+
+The layout works on tmux 3.3 or above, or on Zellij 0.44 or above with fzf
+0.71.0 or above. It is the default on tmux 3.7 or above with fzf 0.74.0 or
+above, and on Zellij, where the pane is not modal: Vim keeps the window fzf
+was started from visible, and you can switch to it while fzf is open. Below
+those versions tmux gives a popup that cannot be left, so a window inside Vim
+is the default there. On tmux, an explicit `--border` style also gives a modal
+popup rather than a floating pane, because the native border of a tmux
+floating pane cannot be removed. Drop `--border` to keep the floating pane and
+its native border. Zellij keeps the floating pane either way, and hides its
+native border when fzf draws one. Set `g:fzf_layout` yourself to choose either
+one.
 
 ```vim
-" See `--popup` option in `man fzf` for available options
-" [center|top|bottom|left|right][,SIZE[%]][,SIZE[%]]
 if exists('$TMUX') || exists('$ZELLIJ')
+  " See `--popup` option in `man fzf` for available options
+  " [center|top|bottom|left|right][,SIZE[%]][,SIZE[%]]
   let g:fzf_layout = { 'popup': '90%,70%' }
 else
-  let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
+  " Configure the Vim popup window in case not on the multiplexer
+  let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.7 } }
 endif
 ```
 
@@ -477,7 +530,8 @@ endif
 
 When fzf starts in a terminal buffer, the file type of the buffer is set to
 `fzf`. So you can set up `FileType fzf` autocmd to customize the settings of
-the window.
+the window. This applies to the layouts that open inside Vim, not to the tmux
+or Zellij pane the default uses, which is not a buffer.
 
 For example, if you open fzf on the bottom on the screen (e.g. `{'down':
 '40%'}`), you might want to temporarily disable the statusline for a cleaner
diff --git a/doc/fzf.txt b/doc/fzf.txt
index 46206282..5828c1e4 100644
--- a/doc/fzf.txt
+++ b/doc/fzf.txt
@@ -14,7 +14,8 @@ FZF - TABLE OF CONTENTS                                            *fzf* *fzf-to
       Global options supported by fzf#wrap  |fzf-global-options-supported-by-fzf#wrap|
     Tips                                    |fzf-tips|
       fzf inside terminal buffer            |fzf-inside-terminal-buffer|
-      Starting fzf in a popup window        |fzf-starting-fzf-in-a-popup-window|
+      Starting fzf in a Vim popup window    |fzf-starting-fzf-in-a-vim-popup-window|
+      Starting fzf in a tmux/Zellij popup window  |fzf-starting-fzf-in-a-tmuxzellij-popup-window|
       Hide statusline                       |fzf-hide-statusline|
     License                                 |fzf-license|
 
@@ -161,19 +162,35 @@ Examples~
       \ 'ctrl-v': 'vsplit' }
 
     " Default fzf layout
-    " - Popup window (center of the screen)
-    let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
+    if exists('$TMUX') || exists('$ZELLIJ')
+      " The Vim plugin will try to open fzf in a tmux or Zellij popup
+      " if possible (requires recent fzf and tmux/zellij) using --popup option,
+      " with the following argument:
+      let g:fzf_layout = { 'popup': '90%,60%' }
+    else
+      " If --popup option is not available, it will open in a popup window inside
+      " Vim (center of the screen)
+      let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
+    endif
 
-    " - Popup window (center of the current window)
+    " Here are some more layout examples:
+
+    " - Tmux or Zellij popup at the bottom 40%
+    let g:fzf_layout = { 'popup': 'bottom,40%' }
+
+    " - Tmux or Zellij popup at the top with a different size
+    let g:fzf_layout = { 'popup': 'top,90%,40%' }
+
+    " - Vim popup window: at the center of the current window (relative)
     let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6, 'relative': v:true } }
 
-    " - Popup window (anchored to the bottom of the current window)
+    " - Vim popup window: anchored to the bottom of the current window
     let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6, 'relative': v:true, 'yoffset': 1.0 } }
 
-    " - down / up / left / right
+    " - Vim split window: down / up / left / right
     let g:fzf_layout = { 'down': '40%' }
 
-    " - Window using a Vim command
+    " - Vim window using a Vim command
     let g:fzf_layout = { 'window': 'enew' }
     let g:fzf_layout = { 'window': '-tabnew' }
     let g:fzf_layout = { 'window': '10new' }
@@ -418,8 +435,8 @@ TIPS                                                                  *fzf-tips*
                                                     *fzf-inside-terminal-buffer*
 
 
-On the latest versions of Vim and Neovim, fzf will start in a terminal buffer.
-If you find the default ANSI colors to be different, consider configuring the
+When fzf is configured to start in a terminal buffer inside Vim or Neovim, you
+may find the default ANSI colors to be different. In that case, configure the
 colors using `g:terminal_ansi_colors` in regular Vim or `g:terminal_color_x`
 in Neovim.
 
@@ -452,8 +469,11 @@ in Neovim.
     endif
 <
 
-< Starting fzf in a popup window >____________________________________________~
-                                            *fzf-starting-fzf-in-a-popup-window*
+< Starting fzf in a Vim popup window >________________________________________~
+                                        *fzf-starting-fzf-in-a-vim-popup-window*
+
+You can configure fzf to start in a Vim popup window by setting the `window`
+key in `g:fzf_layout`.
 >
     " Required:
     " - width [float range [0 ~ 1]] or [integer range [8 ~ ]]
@@ -467,16 +487,33 @@ in Neovim.
     "   - 'rounded' / 'sharp' / 'horizontal' / 'vertical' / 'top' / 'bottom' / 'left' / 'right'
     let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
 <
-Alternatively, you can make fzf open in a popup window (requires tmux 3.3 or
-above, or Zellij 0.44 or above) by putting `--popup` options in `popup` key.
-`tmux` is accepted as a synonym, just as `--tmux` is an alias of `--popup`.
+
+< Starting fzf in a tmux/Zellij popup window >________________________________~
+                                 *fzf-starting-fzf-in-a-tmuxzellij-popup-window*
+
+fzf can also start in a popup of the multiplexer instead of a window inside
+Vim, by putting a `--popup` option value in the `popup` key. `tmux` is
+accepted as a synonym, just as `--tmux` is an alias of `--popup`.
+
+The layout works on tmux 3.3 or above, or on Zellij 0.44 or above with fzf
+0.71.0 or above. It is the default on tmux 3.7 or above with fzf 0.74.0 or
+above, and on Zellij, where the pane is not modal: Vim keeps the window fzf
+was started from visible, and you can switch to it while fzf is open. Below
+those versions tmux gives a popup that cannot be left, so a window inside Vim
+is the default there. On tmux, an explicit `--border` style also gives a modal
+popup rather than a floating pane, because the native border of a tmux
+floating pane cannot be removed. Drop `--border` to keep the floating pane and
+its native border. Zellij keeps the floating pane either way, and hides its
+native border when fzf draws one. Set `g:fzf_layout` yourself to choose either
+one.
 >
-    " See `--popup` option in `man fzf` for available options
-    " [center|top|bottom|left|right][,SIZE[%]][,SIZE[%]]
     if exists('$TMUX') || exists('$ZELLIJ')
+      " See `--popup` option in `man fzf` for available options
+      " [center|top|bottom|left|right][,SIZE[%]][,SIZE[%]]
       let g:fzf_layout = { 'popup': '90%,70%' }
     else
-      let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
+      " Configure the Vim popup window in case not on the multiplexer
+      let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.7 } }
     endif
 <
 
@@ -485,7 +522,8 @@ above, or Zellij 0.44 or above) by putting `--popup` options in `popup` key.
 
 When fzf starts in a terminal buffer, the file type of the buffer is set to
 `fzf`. So you can set up `FileType fzf` autocmd to customize the settings of
-the window.
+the window. This applies to the layouts that open inside Vim, not to the tmux
+or Zellij pane the default uses, which is not a buffer.
 
 For example, if you open fzf on the bottom on the screen (e.g. `{'down':
 '40%'}`), you might want to temporarily disable the statusline for a cleaner
diff --git a/plugin/fzf.vim b/plugin/fzf.vim
index 59a540ef..e0dbd64f 100644
--- a/plugin/fzf.vim
+++ b/plugin/fzf.vim
@@ -140,6 +140,11 @@ function! s:popup_support()
 endfunction
 
 function! s:default_layout()
+  " A floating pane leaves the window fzf was started from visible and
+  " reachable while fzf is open. A popup covers it, inside Vim or not
+  if s:floating_pane()
+    return { 'tmux': '90%,60%' }
+  endif
   return s:popup_support()
         \ ? { 'window' : { 'width': 0.9, 'height': 0.6 } }
         \ : { 'down': '~40%' }
@@ -165,6 +170,12 @@ function! fzf#install()
   if v:shell_error
     throw 'Failed to download fzf: '.script
   endif
+
+  " A new binary invalidates the chosen executable and everything derived from
+  " its version, including whether fzf opens a floating pane. fzf#install() is
+  " also the vim-plug 'do' hook, so this can run long after the first fzf call
+  let [s:versions, s:checked] = [{}, {}]
+  unlet! s:exec s:tmux s:tmux_floating
 endfunction
 
 let s:versions = {}
@@ -257,7 +268,7 @@ function! fzf#exec(...)
 endfunction
 
 " Path to the fzf-tmux script, or an empty string if it is not available. Only
-" the legacy options still need it. --tmux is handled by fzf itself.
+" the legacy options still need it. --popup is handled by fzf itself.
 function! s:fzf_tmux_script()
   if !executable(s:fzf_tmux)
     if !executable('fzf-tmux')
@@ -273,14 +284,7 @@ function! s:tmux_enabled()
     return 0
   endif
 
-  " --tmux covers Zellij as well, where the fzf-tmux script and the tmux
-  " version are irrelevant, but the binary only learned it in 0.71.0
-  if exists('$ZELLIJ')
-    return exists('s:exec')
-          \ && s:compare_versions(s:get_version(s:exec), '0.71.0') >= 0
-  endif
-
-  if !exists('$TMUX')
+  if empty($TMUX) && empty($ZELLIJ)
     return 0
   endif
 
@@ -288,7 +292,21 @@ function! s:tmux_enabled()
     return s:tmux
   endif
 
-  let s:tmux = 0
+  let [s:tmux, s:tmux_floating] = [0, 0]
+
+  " --popup covers Zellij as well, where the fzf-tmux script and the tmux
+  " version are irrelevant. fzf learned it in 0.71.0, and the floating pane
+  " options it passes need Zellij 0.44 or above. fzf checks tmux first, so
+  " this branch is Zellij without tmux. Both non-empty means tmux wins.
+  " empty(), not exists(), to match how fzf reads the two variables
+  if empty($TMUX)
+    let s:tmux =
+          \ s:compare_versions(s:get_version(s:fzf_binary()), '0.71.0') >= 0
+          \ && s:compare_versions(s:zellij_version(), '0.44') >= 0
+    let s:tmux_floating = s:tmux
+    return s:tmux
+  endif
+
   let output = system('tmux -V')
   if v:shell_error
     return s:tmux
@@ -296,9 +314,15 @@ function! s:tmux_enabled()
   " e.g. 'tmux 3.7b', 'tmux next-3.8'
   let ver = matchstr(output, '\d\+\.\d\+')
 
-  " --tmux requires tmux 3.3 or above, and needs no fzf-tmux script
+  " --popup requires tmux 3.3 or above, and needs no fzf-tmux script. The
+  " default layout wants a floating pane, which also needs fzf 0.74.0 or
+  " above. fzf opens a modal popup otherwise. The version here only skips the
+  " probe for servers too old to answer it
   if s:compare_versions(ver, '3.3') >= 0
     let s:tmux = 1
+    let s:tmux_floating = s:compare_versions(ver, '3.7') >= 0
+          \ && s:tmux_floating_pane_info()
+          \ && s:compare_versions(s:get_version(s:fzf_binary()), '0.74.0') >= 0
     return s:tmux
   endif
 
@@ -451,7 +475,10 @@ function! fzf#wrap(...)
     if !exists('g:fzf_layout') && exists('g:fzf_height')
       let opts.down = g:fzf_height
     else
-      let opts = extend(opts, s:validate_layout(get(g:, 'fzf_layout', s:default_layout())))
+      " Not get(), which would evaluate s:default_layout() and run its version
+      " checks even when g:fzf_layout makes the answer irrelevant
+      let opts = extend(opts, s:validate_layout(
+            \ exists('g:fzf_layout') ? g:fzf_layout : s:default_layout()))
     endif
   endif
 
@@ -627,6 +654,57 @@ function! s:present(dict, ...)
   return 0
 endfunction
 
+" The binary fzf#exec() would choose, without its prompting or installing.
+" Layout selection runs before fzf#exec() has resolved one
+function! s:fzf_binary()
+  if exists('s:exec')
+    return s:exec
+  endif
+  let bins = filter(['fzf', s:fzf_go], 'executable(v:val)')
+  if empty(bins)
+    return ''
+  endif
+  return len(bins) > 1 ? sort(bins, 's:compare_binary_versions')[-1] : bins[0]
+endfunction
+
+function! s:zellij_version()
+  if !exists('s:zellij_ver')
+    let output = systemlist('zellij --version')
+    let s:zellij_ver = v:shell_error || empty(output)
+          \ ? '' : matchstr(output[0], '[0-9.]\+')
+  endif
+  return s:zellij_ver
+endfunction
+
+" fzf decides on the running server, not on the version the tmux client
+" reports, so ask it the same question rather than predicting the answer.
+" See tmuxFloatingPaneInfo in src/tmux.go
+function! s:tmux_floating_pane_info()
+  " fzf does not use a floating pane when it was not started from a pane
+  if empty($TMUX_PANE)
+    return 0
+  endif
+  let out = system('tmux display-message -p -t '.fzf#shellescape($TMUX_PANE)
+        \ .' ''#{window_width} #{window_height}'' '';'' list-commands new-pane')
+  " A server that does not know the command exits normally with no output
+  if v:shell_error || out !~# 'new-pane'
+    return 0
+  endif
+  " Too small for a floating pane of the minimum size
+  return str2nr(matchstr(out, '^\s*\zs\d\+')) >= 3
+        \ && str2nr(matchstr(out, '^\s*\d\+\s\+\zs\d\+')) >= 3
+endfunction
+
+" Whether fzf will open a floating pane that can be left while fzf runs. A
+" tmux popup below 3.7 is modal, and the fzf-tmux script that older tmux
+" versions need does not accept a --popup value at all. Without a job to wait
+" on fzf, s:execute_tmux() blocks on system() and the window stays visible but
+" frozen, so the default keeps fzf inside Vim there
+function! s:floating_pane()
+  return (has('nvim') || has('job'))
+        \ && s:tmux_enabled() && get(s:, 'tmux_floating', 0)
+endfunction
+
 function! s:fzf_tmux(dict)
   let size = get(a:dict, 'tmux', '')
   if empty(size)
diff --git a/test/vim/fzf.vader b/test/vim/fzf.vader
index 28115d0b..402a6d99 100644
--- a/test/vim/fzf.vader
+++ b/test/vim/fzf.vader
@@ -102,9 +102,36 @@ Execute (fzf#run with dir option and autochdir when final cwd is same as dir):
   " Working directory changed due to &acd
   AssertEqual '/', getcwd()
 
+Execute (Default layout):
+  unlet! g:fzf_layout g:fzf_height
+  let layout_keys = ['window', 'popup', 'tmux', 'up', 'down', 'left', 'right']
+
+  let opts = fzf#wrap('foobar')
+  Log opts
+  let found = filter(copy(layout_keys), 'has_key(opts, v:val)')
+  AssertEqual 1, len(found)
+  if found[0] ==# 'tmux'
+    " Only where fzf opens a floating pane, which can be left while fzf runs
+    Assert !empty($TMUX) || !empty($ZELLIJ)
+    AssertEqual '90%,60%', opts.tmux
+  elseif found[0] ==# 'window'
+    AssertEqual 0.9, opts.window.width
+  else
+    " No popup support in this build
+    AssertEqual '~40%', opts.down
+  endif
+
+  " Fullscreen strips it, whichever it was
+  let opts = fzf#wrap('foobar', {}, 1)
+  Log opts
+  AssertEqual [], filter(copy(layout_keys), 'has_key(opts, v:val)')
+
 Execute (fzf#wrap):
   AssertThrows fzf#wrap({'foo': 'bar'})
 
+  " Pin the layout so the assertions do not depend on the environment
+  let g:fzf_layout = { 'window': { 'width': 0.9, 'height': 0.6 } }
+
   let opts = fzf#wrap('foobar')
   Log opts
   AssertEqual 0.9, opts.window.width