There several artists called The Fuzz:

1) American vocal trio from Washington DC, USA
2) English band now known as SOLKO
3) American garage rock duo from Westland IL, USA
4) Australian four piece rock band from Perth WA

1) The Fuzz was a short-lived American vocal trio from Washington DC, comprised of Sheila Young (born 08/16/1951), Barbara Gilliam (aka Roberta Gilliam; born 08/16/1952 - died 08/04/2008), and Val Williams (born 03/26/1952). They started out in 1970 as The Passionettes, but changed their name when they signed to Calla Records in 1971.

Their self-titled debut came out that year, and the single "I Love You For All Seasons" went Top 10 R&B and peaked at #21 on the US Billboard Pop Singles chart.The follow-up single, "Like An Open Door", hit #14 on the R&B charts, but further singles had no success and the group split up in 1972.

2) The Fuzz from England are a contemporary and upcoming band known for vibrant, energetic live sets and intelligent songwriting. The band play a Dub/Funk/Rock/Jazz kind of thing.NOTE: The Fuzz are now called 'SOLKO' http://www.last.fm/music/Solko

3) The Fuzz are from Westland, MI, USA on their own Melting Records label. Two dudes making swinging garage rock. It's loud but dance-able. Your toes will tap tap and your head will bang. Jason Bombach and Todd Bruhnsen finally commit to writing together. You have some of Jason's noise weirdness with Todd's accessibility. It's The Fuzz.
dafuzz.bandcamp.com

4) The Fuzz are a four piece rock band from Perth, Western Australia comprising of KT Rumble (Douglas May) (guitar), Shayne Macri (bass) and Ben Mountford (drums) with Abbe May added as vocals. Growing up in Bunbury, Western Australia, they played together during high school and went on to win the WA leg of Triple J Unearthed in 2002 with the track 'The Bomb'.

The Fuzz issued two extended plays, Dead on the Road (2004) and Take the Money (November 2004), and a studio album, 100 Demons (8 August 2005). In October 2005 Dylan McCardle reviewed their CD launch of the latter for PerthSounds.com, which was "a return to simple but powerful formula that is rock 'n' roll ... a night where female vocalists came to the fore, and Abbe May is certainly amongst the cream of the crop. She gave 110% percent with her vocals, she jumped up and down the stage like a woman possessed".

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Artist biography from last.fm