Rapp was already making a name for himself on Broadway when he nabbed the role of Mark in the 1995 off-Broadway cast of Rent. He went on to play Mark on Broadway, a National Tour, and a West End run, as well as reprising the role on film. Rapp has also released a solo CD, a memoir about Rent, and developed a one-man stage show. In 2016, Rapp earned his first regular TV role as Lt. Commander Paul Stamets on Star Trek: Discovery, the first openly gay character in the Star Trek television franchise.