Yup, doesn’t work on a left-click when there are elements inside the frame. But you can use right-click to achieve this, or ⌘right-click if the frame is nested inside other frames.

There are multiple ways you can do it:

1. Cmd/Ctrl + Right Click or simply right click and use the select menu.


2. Click the frame name at the top left corner.


3. Click the frame in the layers panel.


4. Surround the frame in the selection area: drag from above the top corner to the bottom.


5. Select something inside and then press Shift + Enter to select the parent.


6. NEW: Cmd/Ctrl + Left Click the frame (deep select), it will be selected if it has a background.

Personally I use the 2 and 5 methods the most. Since the introduction of #6 I only use it.

And is there also an easy way to toggle through the frames via shortcut without clicking anything?

There are different shortcuts for that! End/Home, N/Shift + N, Tab/Shift + Tab.