Oliver comes from a racing family; his father Ray Oliver had a successful career until his death in a race fall at Kalgoorlie, Western Australia. His elder brother Jason Oliver died on 29 October 2002 after a fall at Belmont Park Racecourse, Western Australia when a young horse he was riding broke both front legs and fell during a race trial. The horse was found to have been administered phenylbutazone prior to the trial and this was thought to be a contributing factor in the accident.
Damien returned to riding in 2006 after serious back injuries sustained in a fall at Moonee Valley, and rode the Japanese horse Pop Rock in the 2006 Melbourne Cup, which finished second to stablemate Delta Blues. In the 2007 Melbourne Cup, he placed second to Efficient on English horse Purple Moon.
Oliver has won the Melbourne Cup on Doriemus (1995) Media Puzzle (2002), the Caulfield Cup on Mannerism (1992), Paris Lane (1994), Doriemus (1995), and Sky Heights (1999), and the Cox Plate on Dane Ripper (1997) and Northerly (2001). He was also the regular rider of Lee Freedman's champion sprinter Schillaci (1991–95) and top filly Alinghi (2003–05). In the 2007 Golden Slipper, Damien completed the grand slam of Australian racing by winning the 2 year old race on the John Hawkes trained Forensics.
On 22 September 2010, Oliver pulled out of rides at a Sandown meeting, while helping police with their inquiries into a criminal investigation.
In 2012, Oliver was accused of placing a $10,000 bet on a rival horse to beat a horse he was riding in the same race. He was subsequently dropped from the Lloyd Williams-owned Green Moon in the Cox Plate and Melbourne Cup. On November 13 Oliver was formally charged with the alleged offence.
- "Jockey Jason Oliver dies", theage.com, 30 October 2002
- Made in Japan: double win a fairytale finish
- 2002 Melbourne Cup result
- Dowsley, Anthony; Dunn, Adrian; Hobbs, Kerri-Ann (22 September 2010), "Star jockey Damien Oliver questioned by police", Herald Sun
- The Age: Oliver's $10,000 secret bet
- "Officials call for stand-down powers". 3 News NZ. 6 November 2012.
- "Damien Oliver charged over betting scandal". 3 News NZ. 13 November 2012.