One of the most important bands that formed in the 80's was R.E.M. They came from post-punk beginnings, but developed in a new direction (that wasn't New Wave). I don't know exactly what to call it, but it eventually became what mainstream pop-rock was.
Nowadays, they have a reputation for being that band that made gentle, thoughtful, non-threatening pop for liberals, such as Losing My Religion (gag!). But when you look over their history, you see they were a serious band with an amazingly intense front man in Michael Stipe. With that distinctive, iconic voice, Stipe was singular in purpose, and often wild on stage.
Their 1983 debut album Murmur won critical accolades, and Radio Free Europe became a hit. They followed with the album Reckoning, which contained the songs Pretty Persuasion, Don't Go Back to Rockville, and So. Central Rain (I'm Sorry). Here's the 2 song set from their TV premier on Letterman. Note that during the interview, Stipe is sitting down behind Peter Buck while Letterman chats with the band. He finally appears as Dave gets ready to go back to his desk.
REM – Radio Free Europe/ So. Central Rain (I’m Sorry) (live on Letterman)
Their next album included Can’t Get There From Here. The one after that contained Fall on Me, and Superman. But it was the 1987 album Document that introduced us to hits like The One I Love, and these next two, shown in these 1999 performances, where Stipe is mixing with the audience.
REM - Finest Worksong (live)
REM – It’s the End of the World as We Know It (live)