By the time Curren hit the ASP World Tour in 1983, he was taking out pros such as Rabbit Bartholomew, Shaun Tomson, and Cheyne Horan. He was world champion three times - 1985, 1986, 1990, and won 33 championship events in his professional career, the latter being a total only bettered by Kelly Slater.

He achieved status both for his competitive drive and for his surfing style. He made a decision to retire from competitive surfing in the mid-1990s. In 1990, at Margaret River, Curren rode a wave all the way from the take-off zone to the Rivermouth - roughly a 1200-foot ride.