For his turn as an American student coming of age overseas in the acclaimed new film Call Me By Your Name, Armie Hammer is earning his first whiff of Oscar buzz. But he didn’t get to the point of receiving critical adulation overnight. The clean-cut up-and-comer cut his teeth with bit parts on television series like Desperate Housewives, played a set of privileged twins (Harvard boys Cameron and Tyler Winklevoss) in The Social Network, and was almost Batman—but alas, Justice League: Mortal was never meant to be. He’s been a big-budget lead as a different sort of superhero, opposite Johnny Depp in The Lone Ranger, and as KGB agent Ilya Kuryakin in the film adaptation of The Man From U.N.C.L.E., but there’s also a surprising amount of indie fare to be found in his filmography. In short, Hammer’s career is one to watch: His best is yet to come.