Curtis' international film credits include Three Kings, Bringing Out the Dead (both 1999), Blow , Training Day (both 2001), Collateral Damage (2002), Sunshine, Live Free or Die Hard (both 2007), Push, Crossing Over (both 2009), Colombiana (2011), and Doctor Sleep (2019), also portraying James "Mac" Mackreides in The Meg (2018) and Meg 2: The Trench (2023) and Tonowari in Avatar: The Way of Water (2022) and the upcoming Avatar: Fire and Ash (2025).

[8] Curtis started acting in amateur productions of musicals Fiddler on the Roof and Man of La Mancha with the Kapiti Players and the Mantis Cooperative Theatre Company, before attending the New Zealand Drama School and Teatro Dimitri Scuola in Switzerland.

He went on to win attention in Once Were Warriors, one of the most successful films released on New Zealand screens; the line "Uncle fucken Bully" referring to Curtis's character spoken by "Jake the Muss", played by Temuera Morrison, became one of New Zealand film's most memorable and quoted lines, as well as being part of the "Kiwiana" trend.

In 2000 Curtis starred as family man Billy Williams in Jubilee,[9] before playing father to the lead character in the international hit Whale Rider.

They have produced several shorts under the new company banner, notably Two Cars, One Night, which received an Academy Award nomination in 2005, and Hawaikii by director Mike Jonathan in 2006.

[11] In 2014, Curtis played the lead role in The Dark Horse, which the National Radio review called "one of the greatest New Zealand films ever made.

"[12] The New Zealand Herald praised him for his "towering performance"[13] as real-life Gisborne speed chess player and coach Genesis Potini, who died in 2011.

Curtis has appeared in the films Martin Scorsese's Bringing Out the Dead (1999), Three Kings (1999), the drug drama Blow (2001) with Johnny Depp, Training Day (2001), Collateral Damage (2002) with Arnold Schwarzenegger, Live Free or Die Hard (2007), Sunshine (2007), Push (2009), “10,000 B.C.” (2008) the re-make, and Colombiana (2011).

[15] In the NBC TV drama Trauma,[16] he played daredevil flight medic Reuben "Rabbit" Palchuck.