Joe Satriani was Steve Vai's Guitar Teacher.
Steve Vai mailed Frank Zappa a transcription of Zappa's "The Black Page", an instrumental song written for drums, along with a tape with some of Vai's guitar playing. Zappa was so impressed with the abilities of the young musician that he hired him in 1979 to do work transcribing several of his guitar solos, including many of those appearing on the Joe's Garage album and the Shut Up 'n' Play Yer Guitar series. These transcriptions were published in 1982 in The Frank Zappa Guitar Book.
Subsequent to being hired as a transcriber, Vai did overdubs on many of the guitar parts for Zappa's album You Are What You Is. Thereafter he became a full-fledged band member, going on his first tour with Zappa in the Autumn of 1980.
Meanwhile, Joe Satriani has filed suit against Coldplay for alleged copyright infringement of one of his songs. Satriani claims Coldplay's Grammy nominated hit "Viva la Vida" copied "substantial, original portions" of his 2004 song, "If I Could Fly."
Joe, Steve Vai, and Eric Johnson playing My Guitar wants to kill Your Mama Live