Even if your smartphone does not have a radio receiver built in, it's still possible to listen to radio with it. To do so, you'll have to access your favourite station's internet stream with an app like TuneIn. The free app for Android, iOS and Windows Phone can bring broadcasters from all over the world to your mobile device.
There are a variety of filter options to help clear the clutter when looking for a genre, city, language or feed from a particular part of the world. A standard UMTS connection is usually enough for a stable signal.
To make sure you don't burn through your metered wireless data plan too quickly, be sure to use the app with a wi-fi connection whenever possible.