Kronos Quartet is a string quartet ensemble consisting of:
Their repertoire consists primarily of contemporary music, with a heavy dose of early music. Some people might describe this as "classical music", which would be misleading; I've never heard them perform any classical or romantic string quartets -- you know, stuff by Haydn, Beethoven, Schubert, Schumann, Tchaikovsky, Borodin, etc. In other words, they are not the Emerson String Quartet, with which they seem to have only Shostakovich in common. However, if you're looking for music by Steve Reich, John Adams, Terry Riley, Philip Glass; Alfred Schnittke; Morton Feldman; Alban Berg, Anton Webern; etc., chances are that Kronos have performed or recorded their music, or even that the music was specifically written for Kronos. They've also dabbled a bit in Jazz (not to their credit, in my opinion), playing compositions by Bill Evans, Thelonius Monk and Ornette Coleman. And then there is the occasional Jimi Hendrix, John Lurie, John Zorn etc.
Kronos spend most of their time touring the globe, giving live performances. In other words, they are not Glenn Gould (apart from the obvious facts that they play different instruments, there's four of them, and they aren't dead). At the same time they manage to record and release more than one CD per year on average. "Winter Was Hard" might be a good CD to "get started", if you're not looking for anything specific.
So what's so special about them? First of all, they play a lot of music that you won't be able to hear anyone else play. Or that wouldn't even exist without them. Second, they are able to play a lot of technically very challenging music. Some of the deliberately repetitive minimalist music they play requires an industrial strength, high endurance string quartet (sometimes even two or three). For example, I didn't believe that it would possible to perform Steve Reich's "Different Trains" live, until I witnessed Kronos pulling it off (tricky, because it calls for two string quartets, so in a live performance there is a virtual second unit, namely Kronos playing on tape, i.e., they are playing with themselves). Finally (ergo?), they can be a very passionate bunch. Just listen to their recording of the Shostakovich String Quartet No. 8 on their album "Black Angels".