diff --git a/react/ActionMenu/Readme.md b/react/ActionMenu/Readme.md
index 7134425ad2..fe902651e8 100644
--- a/react/ActionMenu/Readme.md
+++ b/react/ActionMenu/Readme.md
@@ -74,3 +74,37 @@ const hideMenu = () => setState({ menuDisplayed: false });
   </ActionMenu>}
 </div>
 ```
+
+### Placement
+
+The `placement` and `anchorElRef` prop can be used to control the placement of the menu on desktop. `anchorElRef` should be a ref to a DOM element and not a react component.
+
+```
+import ActionMenu, { ActionMenuItem } from 'cozy-ui/transpiled/react/ActionMenu';
+import Icon from 'cozy-ui/transpiled/react/Icon';
+
+const testRef = React.createRef();
+
+initialState = { menuDisplayed: isTesting() };
+
+const showMenu = () => setState({ menuDisplayed: true });
+const hideMenu = () => setState({ menuDisplayed: false });
+
+const anchorRef = React.createRef();
+
+<div>
+  <button onClick={showMenu} ref={anchorRef}>Show action menu</button>
+  {state.menuDisplayed &&
+    <ActionMenu
+      anchorElRef={anchorRef}
+      placement="bottom-end"
+      buttonRef={testRef}
+      onClose={hideMenu}>
+      <ActionMenuItem left={<Icon icon='file' />}>Item 1</ActionMenuItem>
+  </ActionMenu>}
+</div>
+```
+
+### preventOverflow
+
+Set `preventOverflow` to `true` to keep the ActionMenu visible on desktop, even if `anchorElRef` is outside the viewport.
diff --git a/react/ActionMenu/index.jsx b/react/ActionMenu/index.jsx
index 33a26c869e..e7dba02499 100644
--- a/react/ActionMenu/index.jsx
+++ b/react/ActionMenu/index.jsx
@@ -1,4 +1,4 @@
-import React from 'react'
+import React, { useCallback } from 'react'
 import PropTypes from 'prop-types'
 import cx from 'classnames'
 import ClickAwayListener from '@material-ui/core/ClickAwayListener'
@@ -6,29 +6,58 @@ import styles from './styles.styl'
 import { Media, Bd, Img } from '../Media'
 import BottomDrawer from '../BottomDrawer'
 import withBreakpoints from '../helpers/withBreakpoints'
+import Popper from '@material-ui/core/Popper'
 
-const ActionMenuWrapper = ({ inline, onClose, children }) =>
-  inline ? (
-    <ClickAwayListener onClickAway={onClose}>{children}</ClickAwayListener>
+const ActionMenuWrapper = ({
+  inline,
+  onClose,
+  anchorElRef,
+  placement,
+  preventOverflow,
+  children
+}) => {
+  const getAnchorElement = useCallback(() => {
+    return anchorElRef.current
+  }, [anchorElRef])
+  const normalOverflowModifiers = {
+    preventOverflow: { enabled: false },
+    hide: { enabled: false }
+  }
+
+  return inline ? (
+    <Popper
+      anchorEl={getAnchorElement}
+      modifiers={preventOverflow ? null : normalOverflowModifiers}
+      open
+      placement={placement}
+    >
+      <ClickAwayListener onClickAway={onClose}>{children}</ClickAwayListener>
+    </Popper>
   ) : (
     <BottomDrawer onClose={onClose}>{children}</BottomDrawer>
   )
+}
 
 const ActionMenu = ({
   children,
   className,
   onClose,
+  placement,
+  preventOverflow,
+  anchorElRef,
   breakpoints: { isDesktop }
 }) => {
   const shouldDisplayInline = isDesktop
+  const containerRef = React.createRef()
   return (
-    <div
-      className={cx(
-        { [styles['c-actionmenu-container']]: shouldDisplayInline },
-        className
-      )}
-    >
-      <ActionMenuWrapper onClose={onClose} inline={shouldDisplayInline}>
+    <div className={className} ref={containerRef}>
+      <ActionMenuWrapper
+        onClose={onClose}
+        inline={shouldDisplayInline}
+        anchorElRef={anchorElRef || containerRef}
+        placement={placement}
+        preventOverflow={preventOverflow}
+      >
         <div
           className={cx(styles['c-actionmenu'], {
             [styles['c-actionmenu--inline']]: shouldDisplayInline
@@ -47,7 +76,31 @@ ActionMenu.propTypes = {
   /** Extra class */
   className: PropTypes.string,
   /** What to do on close */
-  onClose: PropTypes.func
+  onClose: PropTypes.func,
+  /** Controls the placement of the menu on desktop */
+  placement: PropTypes.oneOf([
+    'bottom-end',
+    'bottom-start',
+    'bottom',
+    'left-end',
+    'left-start',
+    'left',
+    'right-end',
+    'right-start',
+    'right',
+    'top-end',
+    'top-start',
+    'top'
+  ]),
+  /** Will keep the menu visible when scrolling */
+  preventOverflow: PropTypes.bool,
+  /** The reference element for the menu placement and overflow prevention. */
+  anchorElRef: PropTypes.object
+}
+
+ActionMenu.defaultProps = {
+  placement: 'bottom-start',
+  preventOverflow: false
 }
 
 const ActionMenuHeader = ({ children }) => {
diff --git a/react/ActionMenu/styles.styl b/react/ActionMenu/styles.styl
index ff10660612..37a263c627 100644
--- a/react/ActionMenu/styles.styl
+++ b/react/ActionMenu/styles.styl
@@ -6,9 +6,6 @@
 .c-actionmenu--inline
     @extends $actionmenu--inline
 
-.c-actionmenu-container
-    @extends $actionmenu-container
-
 .c-actionmenu-header
     @extends $actionmenu-header
 
diff --git a/react/BottomDrawer/styles.styl b/react/BottomDrawer/styles.styl
index ebef19fb3f..dc9016446b 100644
--- a/react/BottomDrawer/styles.styl
+++ b/react/BottomDrawer/styles.styl
@@ -1,16 +1,17 @@
 @require 'tools/mixins'
 @require 'settings/spaces'
+@require 'settings/z-index'
 
 .with-transition
     transition transform .1s ease-out
 
 .BottomDrawer-content
-    z-index        $file-action-menu
+    z-index        $drawer-index
     position       fixed
     bottom         rem(9)
     bottom         env(safe-area-inset-bottom) // @stylint ignore
     left           0
-    width          'calc(100% - %s)' % rem(16)
+    width          'calc(100% - %s)' % (spacing_values.m * 2)
     margin         0 spacing_values.m
     padding-bottom rem(5)
     box-sizing border-box
diff --git a/react/Menu/Readme.md b/react/Menu/Readme.md
index 7a06da3278..071916a097 100644
--- a/react/Menu/Readme.md
+++ b/react/Menu/Readme.md
@@ -94,3 +94,12 @@ const showItem = item => {
   </ActionMenu>}
 </div>
 ```
+
+#### `position` and `popover`
+
+`ActionMenu` relies on the Material-UI (Popover)[https://v3.material-ui.com/utils/popper/] component to handle both `position` and `popover`.
+
+- `position='left'` is now `placement='bottom-start'`, and is still the default behavior.
+- `position='right'` is now `placement='bottom-end'`.
+- All other Popover.js placement options are also supported
+- The Menu `popover` prop is now called `preventOverflow`
diff --git a/react/__snapshots__/examples.spec.jsx.snap b/react/__snapshots__/examples.spec.jsx.snap
index 680741141c..2aa8fa9c52 100644
--- a/react/__snapshots__/examples.spec.jsx.snap
+++ b/react/__snapshots__/examples.spec.jsx.snap
@@ -3,7 +3,7 @@
 exports[`ActionMenu should render examples: ActionMenu 1`] = `
 "<div>
   <div><button>Show action menu</button>
-    <div class=\\"styles__c-actionmenu-container___JhthU\\">
+    <div>
       <div class=\\"styles__c-actionmenu___22Fp1 styles__c-actionmenu--inline___1SXZa\\">
         <div class=\\"styles__media___cSJMp styles__c-actionmenu-item___gODqd\\">
           <div class=\\"styles__img___3SHpG u-mh-1\\"><svg class=\\"styles__icon___23x3R\\" width=\\"16\\" height=\\"16\\">
@@ -32,7 +32,7 @@ exports[`ActionMenu should render examples: ActionMenu 1`] = `
 exports[`ActionMenu should render examples: ActionMenu 2`] = `
 "<div>
   <div><button>Show action menu</button>
-    <div class=\\"styles__c-actionmenu-container___JhthU\\">
+    <div>
       <div class=\\"styles__c-actionmenu___22Fp1 styles__c-actionmenu--inline___1SXZa\\">
         <div class=\\"styles__media___cSJMp styles__c-actionmenu-item___gODqd\\">
           <div class=\\"styles__img___3SHpG u-mh-1\\"><svg class=\\"styles__icon___23x3R\\" width=\\"16\\" height=\\"16\\">
@@ -61,7 +61,24 @@ exports[`ActionMenu should render examples: ActionMenu 2`] = `
 exports[`ActionMenu should render examples: ActionMenu 3`] = `
 "<div>
   <div><button>Show action menu</button>
-    <div class=\\"styles__c-actionmenu-container___JhthU\\">
+    <div>
+      <div class=\\"styles__c-actionmenu___22Fp1 styles__c-actionmenu--inline___1SXZa\\">
+        <div class=\\"styles__media___cSJMp styles__c-actionmenu-item___gODqd\\">
+          <div class=\\"styles__img___3SHpG u-mh-1\\"><svg class=\\"styles__icon___23x3R\\" width=\\"16\\" height=\\"16\\">
+              <use xlink:href=\\"#file\\"></use>
+            </svg></div>
+          <div class=\\"styles__bd___1Uv-F u-mr-1\\">Item 1</div>
+        </div>
+      </div>
+    </div>
+  </div>
+</div>"
+`;
+
+exports[`ActionMenu should render examples: ActionMenu 4`] = `
+"<div>
+  <div><button>Show action menu</button>
+    <div>
       <div class=\\"styles__c-actionmenu___22Fp1 styles__c-actionmenu--inline___1SXZa\\">
         <div class=\\"styles__media___cSJMp styles__c-actionmenu-item___gODqd\\">
           <div class=\\"styles__img___3SHpG u-mh-1\\"><svg class=\\"styles__icon___23x3R\\" width=\\"16\\" height=\\"16\\">
diff --git a/react/examples.spec.jsx b/react/examples.spec.jsx
index f2ec5179ec..0291d8894a 100644
--- a/react/examples.spec.jsx
+++ b/react/examples.spec.jsx
@@ -1,6 +1,11 @@
 import testFromStyleguidist from '../test/testFromStyleguidist'
 import path from 'path'
 
+// Popper does not work well inside of jest as it heavily relies on DOM APIs (see https://github.com/popperjs/popper-core/issues/478).
+jest.mock('@material-ui/core/Popper', () => {
+  return ({ children }) => children
+})
+
 const makeRequire = subpath => m => {
   if (m.indexOf('.') === 0) {
     return require('./' + path.join(subpath, m))
diff --git a/stylus/components/action-menu.styl b/stylus/components/action-menu.styl
index 1c3c338c7d..94ef7d5a24 100644
--- a/stylus/components/action-menu.styl
+++ b/stylus/components/action-menu.styl
@@ -1,9 +1,6 @@
 @require './popover.styl'
 @require '../tools/mixins'
 
-$actionmenu-container
-    position relative
-
 $actionmenu
     @extend $popover
 
@@ -11,9 +8,6 @@ $actionmenu
         margin-top 0
 
 $actionmenu--inline
-    position absolute
-    bottom auto
-    left auto
     width auto
     min-width rem(220)
 
diff --git a/stylus/settings/z-index.styl b/stylus/settings/z-index.styl
index 3bffc6ee64..78e87d1bec 100644
--- a/stylus/settings/z-index.styl
+++ b/stylus/settings/z-index.styl
@@ -42,6 +42,7 @@ $bar-index          = $nav-index + 1 // Not actually used, just as reference
 $selection-index    = 30
 $popover-index      = 40
 $overlay-index      = 50
-$file-action-menu   = 60
+$file-action-menu   = 60 // replaced by $drawer-index
+$drawer-index       = 60
 $modal-index        = 70
 $alert-index        = 80