There is more than one artist with this name. Here they are described in order of popularity on Last.fm.
1) Guernica (ゲルニカ), presumably named after the famous painting Guernica by Pablo Picasso, this Japanese trio from the 1980s specializes in avant-garde music in a retro 1920's and 30's cabaret style. Their early recordings are primarily electronic (using synthesizers instead of traditional acoustic instruments) but their later works are performed by a live orchestra.
The primary members of Guernica are:
戸川純 (Jun Togawa) - vocalist
上野耕路 (Koji Ueno) - composer, pianist and violinist
太田螢一 (Keiichi Ohta) - lyricist and art director
2) The Guernica. Handsome young men from the suburbs of Brussels, Belgium. According to them, they play "indie trance", but it is probably more sensible to describe them as avant rock, associating them with bands as Blonde Redhead or Unwound. However, people can and have heard bands like Pavement, American Football, early Trail of Dead, Hood, 90's Sonic Youth, late Fugazi and lots of other indie outfits in the sound which remains their own. A sound with lots of interlocking, arpeggiated and melodic guitars, with varying intensity and a hidden complexity which keeps them relatively accessible. The first Guernica release was released early 2008 on Vlas Vegas Records. It’s called 'Who Are Your Songs For?' and is rocking the music charts all over the belgium.
3) Guernica was a six-piece post-hardcore outfit from Charlotte, NC, active from 2005 to 2009. Blending a variety of influences to form a unique sound, they are primarily known for their intense live performances. Their full length, "Currents", was released in Spring 2008. Their final four track EP, "Untitled" was released in early 2009 to much critical acclaim. Mutually decided to go on indefinite hiatus in mid 2009. aThey have played shows across the southeast with acts such as Giant (Level Plane), A Hero A Fake (Victory), The Fire The Flood (No Sleep), and many more.
4) Guernica is a band from Avellino, IT, formed in 2000 and playing art rock, mixing rock, folk progressive and metal influences; lyrics are often intricate and philosophical, mostly in italian.
5) Guernica was a french punk band in the 80's.
6) Guernica was Czech Heavy/Power Metal Band from Kolin (1994-1998)
7) Guernica was an Irish band active from 1985 since 1989. Guernica took a heavy New Order/Joy Division influence and mixed it with indie/C86/jangle-pop sounds. They also incorporated lighter, rockabilly touches to fantastic effect. After a debut single on Solid, they signed to Idol Records in London and released one acclaimed single (orange and red - 12"). They appeared on TV several times including MT USA ("Americano"), TV Ga Ga ("Americano"), Anything Goes ("New Boy"), Borderline ("Deep Sea Diving") and Megamix ("Homing").