He was married to Robert Plant's daughter Carmen Plant, but they separated in 2010.
Prior to him joining Robert Plant and later with Page and Plant he was a member of Violent Blue with session guitarist Neil Taylor. Jones received a Grammy Award in 2009 as a co-writer of the song "Please Read the Letter" from the album "Raising Sand" by Robert Plant and Alison Krauss. Jones has toured and recorded playing both electric and double bass but is most associated with playing a clear acrylic bass. One of his current gigs is bassist for Goldfrapp. Outside of that he works as a session musician, producer and composer.
On 16 September 2013, Jones released his debut solo album Love Form through Stranger Records.