The son of Mary Lee (née Baird; died 1997) and Douglas Rapp, Adam Rapp was born in Chicago and spent most of his youth in Joliet, Illinois. His mother died of cancer at age 55 in 1997.
He is a graduate of St. John's Military Academy (Delafield, Wisconsin) and Clarke College (Dubuque, Iowa), where he captained the varsity basketball team. After college he moved to New York City's East Village, where he landed a day job in book publishing and wrote fiction and plays at night. He later completed a two-year playwriting fellowship at The Juilliard School. His younger brother is actor and singer Anthony Rapp.
Rapp attended the O'Neill Playwrights Conference in 1996. His play Finer Noble Gases was staged by the Eugene O'Neill Theatre in 2000, by Actors Theatre of Louisville in 2001, by Carolina Actors Studio Theatre in Charlotte in 2003, and by Rattlestick Playwrights Theater in New York City in 2004. In 2001, Nocturne was premiered by the New York Theatre Workshop. It has also been staged at by American Repertory Theater and Berkeley Repertory Theatre. His play Stone Cold Dead Serious was produced in 2002 by the American Repertory Theater.
Rapp's Red Light Winter received the Joseph Jefferson Award (Best New Work) in 2005 for its production at Steppenwolf Theatre Company. The play was also a finalist for the Pulitzer Prize for Drama in 2006. Rapp directed a production of Los Angeles, by Julian Sheppard, in 2007 at the Flea Theatre. As of 2007, he was Resident Playwright at the Edge Theatre Company in New York City.
He teaches at the Yale School of Drama. In 2011, Rapp's The Metal Children was given its regional debut by Swine Palace on Louisiana State University's campus.
The majority of Rapp's plays feature small casts and are set in small spaces. Many characters in the plays are lower-class Americans. His plays often combine stories of Midwestern longing with the idea of finding escape in New York. He combines humor with gloom, preferring dark themes
In a conversation with fellow playwright Gina Gionfriddo published in The Brooklyn Rail, Rapp says: "When you see something powerfully acted on stage, it hits a nerve in the way music hits a nerve … Watching someone twelve feet from you falling in love or being abused … There’s something raw about that experience that you don’t get from film or TV."
Rapp's first young adult novel, Missing the Piano, was published in 1994. After writing his second book, The Buffalo Tree, in 1999, Rapp was invited to be the first author in residence at Ridgewood High School. The Buffalo Tree was censored by the Muhlenberg School Board in Reading, Pennsylvania due to its themes, graphic language and sexual content. His 2003 novel 33 Snowfish was one of Young Adult Library Services Association's Top Ten Best Books for Young Adults. He released Under the Wolf, Under the Dog in 2004.
His first adult novel, The Year of Endless Sorrows, was released in 2006. Rapp made his graphic novel debut with the release of Ball Peen Hammer in September 2009. His second graphic novel, "Decelerate Blue" was published in February 2017.
Rapp directed his first film, Winter Passing with Zooey Deschanel and Will Ferrell (2005), and was a creative consultant for the television show The L Word.
While working on The L Word, Rapp left in the middle of the season to attend the Edinburgh Festival, where he directed his play, Finer Noble Gases, which won the Fringe First Award. He wrote for the 2010 season of HBO's In Treatment.
He was a member of the band Bottomside, which released the independent CD The Element Man in September 2004. He is a member of "Less the Band", which released the album Bear in April 2006.