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. He then had to walk back to Mainbreak from the Rivermouth to re-enter the surf. Those who saw it say it has never been repeated, in or out of competition.
Curren still surfs in contests on the ASP World Qualifying Series (WQS.) He is also often invited to surf in World Championship Tour (WCT) trials or contests as a wildcard. He has competed in the Annual Switchfoot Bro-Am Surf Contest for 3 years in a row, surfing on the Switchfoot team.
In his five-year rise to World Surfing Champion Curren appeared under a contract with surfboard company Channel Islands. He co-producing and rode pro surfboard models such as the Black Beauty and the Red Beauty.
Early in his professional career he signed with OP swimwear then later changed sponsorships deals to Rip Curl Wetsuits and Clothing.