In 15.0.70, look in the tree at Audio > Connected Media > various channels
To add your own website/ URL, right-click on "Connected Media" in the tree.
Or, in the main window, go to the desired online "radio". Then click the pulldown of the tab of that window, and select Add Website to save the current URL and specify a suitable name.
In some cases, all you can do is store a URL that takes you to a site where you then must use the site's player, so you'll lose it if you close the tab. In other cases, you might have to do some clicking but then the audio will start "in MC" -- you don't have to keep the tab open.
You might discover that you can get get multiple streams going at once, one in MC and the others use site players (quick path to insanity). To stop what MC is streaming, click MC Player's STOP button.