I am a big fan of the band Muse.  They are a British band and began back in 1994.  
What kind of genre are they?
They are a variety of music styles.  There first album really showed off a melancholic alternative rock style.  It was called Showbiz
Hmm.. interesting. Are they grungeish, like Nirvana?
They have a little bit of that.  But they are not as much grunge as the 90s bands of Pearl Jam and Alice and Chains