Audioslave is a rock supergroup consisting of Chris Cornell (former frontman of Soundgarden) and the instrumentalists of Rage Against the Machine. Tom Morello plays guitar, Tim Commerford plays bass, and Brad Wilk drums. As with Rage Against the Machine, the band prides itself on the fact that all sounds are produced using only vocals, guitar, bass guitar, and drums.
Lead singer Chris Cornell released a solo album, Euphoria Morning, in the midst between his leaving Soundgarden and forming Audioslave. Cornell recorded the theme song to the James Bond film, Casino Royale, and will provide a song for the upcoming Lionsgate thriller Bug. He will release his second solo album in 2007. 
Guitarist Tom Morello also performs solo under the name The Nightwatchman, though he has yet to release or announce a solo album. Recently announced on the official Nightwatchman page, Guitarist/Vocalist Tom Morello will release the first CD under the Nightwatchman moniker in the near future.
Bassist Tim Commerford and Drummer Brad Wilk have recently been in the studio together recording some Bass/Drums only tracks. Currently there is no word on a CD release.
Tom Morello described the origin of the name to LAUNCHcast:
While Rage Against the Machine's music was politically influenced, Audioslave's originally was not, as Chris Cornell said he did not want to become the new singer of Rage Against The Machine and needed the freedom to write lyrics which were not overtly political. However, some songs on their newest album, Revelations, are politically influenced, which was explained by Cornell that he always try to evoke his feelings into lyrics with no matter of subject. The band is part of the Axis of Justice, which is a non-profit organization formed by Morello and Serj Tankian of System of a Down. Its purpose is to "bring together musicians, fans of music, and grassroots political organizations to fight for social justice together."