There is also an app called "radiodroid" (or maybe it is "radiodroid2"; on the https://f-droid.org app store that says it builds all the apps from free/open source) which I have very much enjoyed for this. Unlike the other 1-2 internet radio apps I tried, this one made it easy to browse thousands of stations, search by tag (I guess everything is in there), language, country, etc etc, set bookmarks, list listening history, and no annoying weirdness. Very few that I have tried had commercials, those that did were not enough to annoy: bach, beatles, ethnic, deep lounge, 1940's big band, tejano, on and on.

Edit: I also recall a nice little linux program called radiotray, on debian (that sat in the XFCE or maybe LXDE app tray / bar), that did something similar. Presumably there are others.

Edit2: I mention radiodroid and internet radio among ideas like watching news TV sites on the internet from around the world, on my simple fun/relaxation page: http://lukecall.net/e-9223372036854618463.html

Edit3: I tried libre.fm too (which basically seems to be an FSF initiative to flag or play favorite tracks from archive.org by category, and had high hopes, thought it had promising ideas, but though it seemed to work well at first, I later couldn't get anything to happen after I logged in, etc., and finally gave up. Mentioning in case others know better.