Law's notable films include Gattaca, Enemy at the Gates, Steven Spielberg's A.I. Artificial Intelligence, Road to Perdition, Alfie, Mike Nichols' Closer, I Heart Huckabees, The Holiday, Contagion, Martin Scorsese's Hugo, Joe Wright's Anna Karenina, Steven Soderbergh's Side Effects, Wes Anderson's The Grand Budapest Hotel, and Paul Feig's Spy. He also portrayed John Watson in Guy Ritchie's Sherlock Holmes and Sherlock Holmes: A Game of Shadows. In 2017, he portrayed the fictional Pope Pius XIII in the HBO drama miniseries The Young Pope.
Law has also had an accomplished career on stage, and has received nominations for three Laurence Olivier Awards and two Tony Awards. He has performed in several West End and Broadway productions.
For Disney, he played Steven Grlcz in Immortality (aka The Wisdom of Crocodiles), Ted Pikul in eXistenZ, Dickie Greenleaf in The Talented Mr. Ripley, Inman in Cold Mountain, Errol Flynn in The Aviator, Will in Breaking and Entering, and Yon-Rogg in Captain Marvel.