You can access your five most recent My Maps and Maps Engine maps in the new Google Maps. To quickly get to your custom maps:
* Open Google Maps and make sure you're signed-in.
* Click into the searchbox.
* Click the 'My custom maps' suggestion that appears below.
* Click the name of the map you want to view. Your map will either open in My Maps or Maps Engine.
You can also still access all of your My Maps and My Places content (available through classic Maps). To get there from the new Google Maps, click the Gear icon gear menu in the bottom right and select My Places.
December 12, 2013
Custom Maps in the New Google Maps
The new version of Google Maps constantly brings back features from the classic Google Maps, which shows that it's almost ready to become the default interface. The new Google Maps shows a link for your custom maps below the search box. If you click the link, you should see a list of custom maps created with Maps Engine Lite or My Maps.