They're considered the kings of goth, although they don't like being referred to or labeled as that. One reason is a lot of people label bands too much & they like a lot of punk bands preferred to be just called rock & roll. Bauhaus the name was named after an art movement of the same name. If you'd like one the perfect collections I'd recommend getting the 3cd japanese import collection titled "Spirit", which is the same title of one of their songs. It's a good place to start to have a lot of their material together although it does miss some of their other good songs like "Rosegarden Funeral of Sores" for example but that song by the way is actually a cover of a John Cale song which John Cale along with Lou Reed, Nico, Sterling Morrison & others is from an old garage/early punk group from the 60's named Velvet Underground. They covered other songs too like Iggy Pop's "The Passenger", Dead Can Dance's Severance, which aren't on that 3cd set. Anyway on that set along with many other songs is one of their bigger songs called "Bela Lugosi's Dead", which helped earn them the title of godfathers & kings of goth. That song was one the main & biggest selling songs on a soundtrack for a vampire movie, That starred David Bowie, Susan Sarandon & Cathrine Deneuve called "The Hunger". As the others mentioned the group split up for a long period which they have had reunions a little bit here & there but not permanent ones. Groups that came out of it was Tones on Tail, Love & Rockets & Dali's Car. Peter Murphy, Daniel Ash & David J all have solo albums also & have worked with others. Here's examples of their various works--
"Bela Lugosi's Dead" clip from the movie "The Hunger"--
http://www.youtube.com/watch?v=zq7xyjU-jsU
"Ziggy Stardust" cover they did of David Bowie's song--
http://www.youtube.com/watch?v=6a_YQXFs7Ts
"Dark Entries"--
http://www.youtube.com/watch?v=SJCuF6cJGVs
Here's Love & Rockets with their "Ball of Confusion"(also a cover)--
http://www.youtube.com/watch?v=-ALRLZQf42s
Peter Murphy solo with "Cuts You Up"--
http://www.youtube.com/watch?v=udQcrUY515A
Favorite Bauhaus songs--"ST Vitus Dance" or "Bela Lugosi's Dead" I think.