diff --git a/bower.json b/bower.json
index 114b4ab1a..ae39400c5 100644
--- a/bower.json
+++ b/bower.json
@@ -5,7 +5,7 @@
     "backbone": "components/backbone#~1.2",
     "bootstrap": "components/bootstrap#~3.3",
     "bootstrap-tour": "0.9.0",
-    "codemirror": "~5.8",
+    "codemirror": "~5.14",
     "es6-promise": "~1.0",
     "font-awesome": "components/font-awesome#~4.2.0",
     "google-caja": "5669",
diff --git a/notebook/static/base/js/utils.js b/notebook/static/base/js/utils.js
index 49178cfd4..cf9ed588a 100644
--- a/notebook/static/base/js/utils.js
+++ b/notebook/static/base/js/utils.js
@@ -946,6 +946,22 @@ define([
         }
     };
 
+    // Test if a drag'n'drop event contains a file (as opposed to an HTML
+    // element/text from the document)
+    var dnd_contain_file = function(event) {
+        // As per the HTML5 drag'n'drop spec, the dataTransfer.types should
+        // contain one "Files" type if a file is being dragged
+        // https://www.w3.org/TR/2011/WD-html5-20110113/dnd.html#dom-datatransfer-types
+        if (event.dataTransfer.types) {
+            for (var i = 0; i < event.dataTransfer.types.length; i++) {
+                if (event.dataTransfer.types[i] == "Files") {
+                    return true;
+                }
+            }
+        }
+        return false;
+    };
+
     var utils = {
         is_loaded: is_loaded,
         load_extension: load_extension,
@@ -990,6 +1006,7 @@ define([
         time: time,
         format_datetime: format_datetime,
         datetime_sort_helper: datetime_sort_helper,
+        dnd_contain_file: dnd_contain_file,
         _ansispan:_ansispan
     };
 
diff --git a/notebook/static/notebook/js/textcell.js b/notebook/static/notebook/js/textcell.js
index c6772b9fc..64d613710 100644
--- a/notebook/static/notebook/js/textcell.js
+++ b/notebook/static/notebook/js/textcell.js
@@ -110,6 +110,7 @@ define([
         inner_cell.append(input_area).append(render_area);
         cell.append(inner_cell);
         this.element = cell;
+        this.inner_cell = inner_cell;
     };
 
 
@@ -282,6 +283,9 @@ define([
         TextCell.apply(this, [$.extend({}, options, {config: config})]);
 
         this.cell_type = 'markdown';
+
+        // Used to keep track of drag events
+        this.drag_counter = 0;
     };
 
     MarkdownCell.options_default = {
@@ -363,6 +367,11 @@ define([
      * @method render
      */
     MarkdownCell.prototype.render = function () {
+        // We clear the dropzone here just in case the dragenter/leave
+        // logic of bind_events wasn't 100% successful.
+        this.drag_counter = 0;
+        this.inner_cell.removeClass('dropzone');
+
         var cont = TextCell.prototype.render.apply(this);
         if (cont) {
             var that = this;
@@ -449,19 +458,44 @@ define([
             }
         });
 
-        // Allow drop event if the dragged file can be used as an attachment
-        this.code_mirror.on("dragstart", function(cm, evt) {
-            var files = evt.dataTransfer.files;
-            for (var i = 0; i < files.length; ++i) {
-                var file = files[i];
-                if (attachment_regex.test(file.type)) {
-                    return false;
-                }
+        // Allow drag event if the dragged file can be used as an attachment
+        // If we use this.code_mirror.on to register a "dragover" handler, we
+        // get an empty dataTransfer
+        this.code_mirror.on("dragover", function(cm, evt) {
+            if (utils.dnd_contain_file(evt)) {
+                evt.preventDefault();
             }
-            return true;
+        });
+
+        // We want to display a visual indicator that the drop is possible.
+        // The dragleave event is fired when we hover a child element (which
+        // is often immediatly after we got the dragenter), so we keep track
+        // of the number of dragenter/dragleave we got, as discussed here :
+        // http://stackoverflow.com/q/7110353/116067
+        // This doesn't seem to be 100% reliable, so we clear the dropzone
+        // class when the cell is rendered as well
+        this.code_mirror.on("dragenter", function(cm, evt) {
+            if (utils.dnd_contain_file(evt)) {
+                that.drag_counter++;
+                that.inner_cell.addClass('dropzone');
+            }
+            evt.preventDefault();
+            evt.stopPropagation();
+        });
+
+        this.code_mirror.on("dragleave", function(cm, evt) {
+            that.drag_counter--;
+            if (that.drag_counter <= 0) {
+                that.inner_cell.removeClass('dropzone');
+            }
+            evt.preventDefault();
+            evt.stopPropagation();
         });
 
         this.code_mirror.on("drop", function(cm, evt) {
+            that.drag_counter = 0;
+            that.inner_cell.removeClass('dropzone');
+
             var files = evt.dataTransfer.files;
             for (var i = 0; i < files.length; ++i) {
                 var file = files[i];
diff --git a/notebook/static/notebook/less/textcell.less b/notebook/static/notebook/less/textcell.less
index 6e3f6ee85..3f49e8b24 100644
--- a/notebook/static/notebook/less/textcell.less
+++ b/notebook/static/notebook/less/textcell.less
@@ -48,6 +48,11 @@ h1,h2,h3,h4,h5,h6 {
     display:none;
 }
 
+.text_cell .dropzone .input_area {
+  border: 2px dashed #bababa;
+  margin: -1px;
+}
+
 .cm-header-1,
 .cm-header-2,
 .cm-header-3,