Miranda was born in New York City and raised in the neighborhood of Inwood, the son of Luz Towns, a clinical psychologist, and Luis A. Miranda, Jr., a Democratic Party consultant who advised New York City mayor Ed Koch. Miranda has one older sister, Luz, who is the Chief Financial Officer of the MirRam Group. During childhood and his teens, he spent at least one month each year with his grandparents in Vega Alta, Puerto Rico. He is of mostly Puerto Rican descent.

Miranda co-wrote the music and lyrics for Bring It On: The Musical with Tom Kitt and Amanda Green. Bring It On premiered at the Alliance Theatre in Atlanta, Georgia in January 2011. The musical began a US national tour on October 30, 2011 in Los Angeles, California. It then played a limited engagement on Broadway at the St. James Theatre, beginning previews on July 12, and officially opening on August 1, 2012. It closed on December 30, 2012. It was nominated for Tony Awards in the categories of Best Musical and Best Choreography.  In 2011, Miranda appeared on the TV series Modern Family in the episode "Good Cop Bad Dog". He appeared as Charley in an Encores! staged concert of Merrily We Roll Along at New York City Center in February 2012. Later that year, he appeared in a small role in The Odd Life of Timothy Green as Reggie and played the recurring role Ruben Marcado on the 2013 NBC drama Do No Harm.  In 2013, Miranda appeared in the episode "Bedtime Stories" (Season 9, Episode 11) on the CBS sitcom How I Met Your Mother. Later that year, he submitted a six-song demo package to Walt Disney Animation Studios; in spring 2014, the studio hired him to help write the songs for its 2016 animated feature film, Moana. In 2014, he performed with comedy duo The Skivvies, and participated in This American Life at the Brooklyn Academy of Music on June 7, 2014 and broadcast on the radio on June 20, 2014, writing the music and lyrics for, and playing The Narrator in, the one-act 21 Chump Street: The Musical. Also in 2014, Miranda appeared in the Encores! revival of Tick, Tick... Boom! under the artistic direction of Jeanine Tesori. The show was directed by Oliver Butler. Miranda won a 2014 Emmy Award for co-composing (with Tom Kitt) the song "Bigger!", the opening number at the 67th Tony Awards in 2013.

what was her greatest accomplishment?
in spring 2014, the studio hired him to help write the songs for its 2016 animated feature film, Moana.