Radio stations that played music had very little change after Television was invented. However, radio plays, dramas and soap operas became nearly extinct. Several popular radio programs, like "Gun Smoke" moved to prime time television and many soap operas moved to day time television. For radio stations, that did not play music, they transitioned to talk radio formats. Some went all news, all the time, some concentrated on sports talk, and Rush Limbaugh saved AM radio by making political talk shows popular. Sports continued to be played on the radio, although the number of listeners to live sporting events take a sharp decline, if those sports are also shown on TV.
Richard Sarnoff, the president of the Radio Corporation of America, thought FM radio would be the salvation of the radio industry. However, it was not until the early 1970s when album oriented rock and roll stations came up with a format that made FM station commercially viable. Also, after 1970, FM radios became standard features on new cars. That made drive time radio financially lucrative to radio stations. Yet, lets not get carried away here. Television advertisements were always more expensive than radio ads, so radio stations did take a massive hit in their revenue streams.
Source: "Empires of the Air: The men who made Radio" a PBS documentary and companion book, by Ken Burns (1991)