Buckingham's career began in the early 1970's with his folk duo Buckingham Nicks (with then girlfriend Stevie Nicks), but he rose to fame as the guitarist and in-band producer for Fleetwood Mac. While his first LP with Fleetwood Mac was a resounding success, the second one (Rumours) was a blockbuster. Rumours remains the sixth best selling album in the U.S. ever -- it was a epic commercial and critical success.
Unfortunately, the commercial success of Fleetwood Mac did not alleviate the band's problems. In fact, it may have added to the issues. In addition to rampant drug use and breakups, Buckingham felt creatively constrained by the standard pop format, and started exploring more interesting sounds. For Fleetwood Mac, this led to the Tusk LP, and it meant that Buckingham's solo work in the early 1980's was creative and interesting. As is often the case, though, this also led to less commercial success. The Go Insane album peaked at #45, while the single of the same name reached #23.
Buckingham would return to Fleetwood Mac for their 1987 album, Tango in the Night, before leaving the band. He then returned in 1997 and has been with the band since then.
Cool trivia fact: One of the guitarists who replaced Lindsey Buckingham in Fleetwood Mac was Billy Burnette, whose song "In Just a Heartbeat" was featured on ERV in February 2012.