Index: src/wp-admin/css/media.css
===================================================================
--- src/wp-admin/css/media.css	(revision 40334)
+++ src/wp-admin/css/media.css	(working copy)
@@ -469,7 +469,7 @@
 .upload-php .mode-grid .media-sidebar {
 	position: relative;
 	width: auto;
-	margin-bottom: 16px;
+	margin-top: 12px;
 	padding: 0 16px;
 	border-left: 4px solid #dd3d36;
  	-webkit-box-shadow: 0 1px 1px 0 rgba(0, 0, 0, 0.1);
@@ -526,7 +526,7 @@
 	left: auto;
 	bottom: auto;
 	padding-top: 0;
-	margin-top: 0;
+	margin-top: 20px;
 	border: 4px dashed #b4b9be;
 }
 
Index: src/wp-admin/upload.php
===================================================================
--- src/wp-admin/upload.php	(revision 40334)
+++ src/wp-admin/upload.php	(working copy)
@@ -77,7 +77,7 @@
 
 		<?php
 		if ( current_user_can( 'upload_files' ) ) { ?>
-			<a href="<?php echo admin_url( 'media-new.php' ); ?>" class="page-title-action"><?php echo esc_html_x( 'Add New', 'file' ); ?></a><?php
+			<a href="<?php echo admin_url( 'media-new.php' ); ?>" class="page-title-action aria-button-if-js"><?php echo esc_html_x( 'Add New', 'file' ); ?></a><?php
 		}
 		?>
 
Index: src/wp-includes/css/media-views.css
===================================================================
--- src/wp-includes/css/media-views.css	(revision 40334)
+++ src/wp-includes/css/media-views.css	(working copy)
@@ -1133,22 +1133,31 @@
 	border: 0;
 	cursor: pointer;
 	height: 48px;
+	outline: none;
+	padding: 0;
 	position: absolute;
-	right: 0;
+	right: 2px;
 	text-align: center;
-	top: 0;
-	width: 50px;
+	top: 2px;
+	width: 48px;
 	z-index: 1;
 }
 
 .uploader-inline .close:before {
-	font: normal 30px/50px dashicons !important;
-	color: #72777c;
+	font: normal 30px/1 dashicons !important;
+	color: #555d66;
 	display: inline-block;
 	content: "\f335";
 	font-weight: 300;
+	margin-top: 1px;
 }
 
+.uploader-inline .close:focus {
+	outline: 1px solid  #5b9dd9;
+	-webkit-box-shadow: 0 0 3px rgba( 0, 115, 170, .8 );
+	box-shadow: 0 0 3px rgba( 0, 115, 170, .8 );
+}
+
 .attachments-browser.hide-sidebar .attachments,
 .attachments-browser.hide-sidebar .uploader-inline {
 	right: 0;
Index: src/wp-includes/js/media/views/attachments/browser.js
===================================================================
--- src/wp-includes/js/media/views/attachments/browser.js	(revision 40334)
+++ src/wp-includes/js/media/views/attachments/browser.js	(working copy)
@@ -40,17 +40,33 @@
 
 		this.controller.on( 'toggle:upload:attachment', this.toggleUploader, this );
 		this.controller.on( 'edit:selection', this.editSelection );
-		this.createToolbar();
+
 		// In the Media Library, the sidebar is used to display errors before the attachments grid.
 		if ( this.options.sidebar && 'errors' === this.options.sidebar ) {
 			this.createSidebar();
 		}
+
+		/*
+		 * For accessibility reasons, place the Inline Uploader before other sections.
+		 * This way, in the Media Library, it's right after the Add New button, see ticket #37188.
+		 */
 		this.createUploader();
+
+		/*
+		 * Create a multi-purpose toolbar. Used as main toolbar in the Media Library
+		 * and also for other things, for example the "Drag and drop to reorder" and
+		 * "Suggested dimensions" info in the media modal.
+		 */
+		this.createToolbar();
+
+		// Create the list of attachments.
 		this.createAttachments();
+
 		// For accessibility reasons, place the normal sidebar after the attachments, see ticket #36909.
 		if ( this.options.sidebar && 'errors' !== this.options.sidebar ) {
 			this.createSidebar();
 		}
+
 		this.updateContent();
 
 		if ( ! this.options.sidebar || 'errors' === this.options.sidebar ) {
@@ -343,7 +359,7 @@
 			canClose:   this.controller.isModeActive( 'grid' )
 		});
 
-		this.uploader.hide();
+		this.uploader.$el.addClass( 'hidden' );
 		this.views.add( this.uploader );
 	},
 
Index: src/wp-includes/js/media/views/frame/manage.js
===================================================================
--- src/wp-includes/js/media/views/frame/manage.js	(revision 40334)
+++ src/wp-includes/js/media/views/frame/manage.js	(working copy)
@@ -38,8 +38,12 @@
 		this.$body = $( document.body );
 		this.$window = $( window );
 		this.$adminBar = $( '#wpadminbar' );
+		// Store the Add New button for later reuse in wp.media.view.UploaderInline.
+		this.$uploaderToggler = $( '.page-title-action' )
+			.attr( 'aria-expanded', 'false' )
+			.on( 'click', _.bind( this.addNewClickHandler, this ) );
+
 		this.$window.on( 'scroll resize', _.debounce( _.bind( this.fixPosition, this ), 15 ) );
-		$( document ).on( 'click', '.page-title-action', _.bind( this.addNewClickHandler, this ) );
 
 		// Ensure core and media grid view UI is enabled.
 		this.$el.addClass('wp-core-ui');
Index: src/wp-includes/js/media/views/uploader/inline.js
===================================================================
--- src/wp-includes/js/media/views/uploader/inline.js	(revision 40334)
+++ src/wp-includes/js/media/views/uploader/inline.js	(working copy)
@@ -119,9 +119,18 @@
 	},
 	show: function() {
 		this.$el.removeClass( 'hidden' );
+		if ( this.controller.$uploaderToggler.length ) {
+			this.controller.$uploaderToggler.attr( 'aria-expanded', 'true' );
+		}
 	},
 	hide: function() {
 		this.$el.addClass( 'hidden' );
+		if ( this.controller.$uploaderToggler.length ) {
+			this.controller.$uploaderToggler
+				.attr( 'aria-expanded', 'false' )
+				// Move focus back to the toggle button when closing the uploader.
+				.focus();
+		}
 	}
 
 });
Index: src/wp-includes/js/media-grid.js
===================================================================
--- src/wp-includes/js/media-grid.js	(revision 40334)
+++ src/wp-includes/js/media-grid.js	(working copy)
@@ -623,8 +623,12 @@
 		this.$body = $( document.body );
 		this.$window = $( window );
 		this.$adminBar = $( '#wpadminbar' );
+		// Store the Add New button for later reuse in wp.media.view.UploaderInline.
+		this.$uploaderToggler = $( '.page-title-action' )
+			.attr( 'aria-expanded', 'false' )
+			.on( 'click', _.bind( this.addNewClickHandler, this ) );
+
 		this.$window.on( 'scroll resize', _.debounce( _.bind( this.fixPosition, this ), 15 ) );
-		$( document ).on( 'click', '.page-title-action', _.bind( this.addNewClickHandler, this ) );
 
 		// Ensure core and media grid view UI is enabled.
 		this.$el.addClass('wp-core-ui');
Index: src/wp-includes/js/media-views.js
===================================================================
--- src/wp-includes/js/media-views.js	(revision 40334)
+++ src/wp-includes/js/media-views.js	(working copy)
@@ -3771,17 +3771,33 @@
 
 		this.controller.on( 'toggle:upload:attachment', this.toggleUploader, this );
 		this.controller.on( 'edit:selection', this.editSelection );
-		this.createToolbar();
+
 		// In the Media Library, the sidebar is used to display errors before the attachments grid.
 		if ( this.options.sidebar && 'errors' === this.options.sidebar ) {
 			this.createSidebar();
 		}
+
+		/*
+		 * For accessibility reasons, place the Inline Uploader before other sections.
+		 * This way, in the Media Library, it's right after the Add New button, see ticket #37188.
+		 */
 		this.createUploader();
+
+		/*
+		 * Create a multi-purpose toolbar. Used as main toolbar in the Media Library
+		 * and also for other things, for example the "Drag and drop to reorder" and
+		 * "Suggested dimensions" info in the media modal.
+		 */
+		this.createToolbar();
+
+		// Create the list of attachments.
 		this.createAttachments();
+
 		// For accessibility reasons, place the normal sidebar after the attachments, see ticket #36909.
 		if ( this.options.sidebar && 'errors' !== this.options.sidebar ) {
 			this.createSidebar();
 		}
+
 		this.updateContent();
 
 		if ( ! this.options.sidebar || 'errors' === this.options.sidebar ) {
@@ -4074,7 +4090,7 @@
 			canClose:   this.controller.isModeActive( 'grid' )
 		});
 
-		this.uploader.hide();
+		this.uploader.$el.addClass( 'hidden' );
 		this.views.add( this.uploader );
 	},
 
@@ -8210,9 +8226,18 @@
 	},
 	show: function() {
 		this.$el.removeClass( 'hidden' );
+		if ( this.controller.$uploaderToggler.length ) {
+			this.controller.$uploaderToggler.attr( 'aria-expanded', 'true' );
+		}
 	},
 	hide: function() {
 		this.$el.addClass( 'hidden' );
+		if ( this.controller.$uploaderToggler.length ) {
+			this.controller.$uploaderToggler
+				.attr( 'aria-expanded', 'false' )
+				// Move focus back to the toggle button when closing the uploader.
+				.focus();
+		}
 	}
 
 });