Shum spent most of his schooling years in the San Luis Obispo area, California and graduated from Arroyo Grande High School in 2000. Initially, he had been more interested in theater and sports but found a passion for dance after auditioning for his high school dance team on a dare. Shum attended San Francisco State University for a year, before dropping out to pursue a dance career. In an interview, he said that his earliest motivations to dance were from watching Ginuwine, Dru Hill and Usher, before becoming influenced by dancers like Gene Kelly and Michael Jackson.

Shum began his dance career in Los Angeles. As a 18-year-old, he was spotted by choreographers Rosero McCoy and Jamal Sims to go on a UK tour with the singer Kaci. He steadily built his career, appearing as the only male dancer on BET’s Comic View, and starred in a series of Apple iPod advertisements as dancing silhouettes. He joined Beyoncé, Alicia Keys and Missy Elliott in their co-headlining tour Ladies First in 2004, while working as a backup dancer for artists including Jennifer Lopez, Jessica Simpson and Mariah Carey. He appeared in several music videos of songs including Lose My Breath by Destiny’s Child and It’s Like That by Mariah Carey. Shum also worked as a dance instructor.

Shum began a relationship with actress and dancer Shelby Rabara in 2007. The two were engaged in October 2013 while on vacation in Hawaii and were married on November 22, 2015 in Costa Rica. The birth of their daughter, Xia, was announced on March 28, 2019.

Since 2008, Shum was given roles in Step Up 2 and later Step Up 3D, both directed by Jon M. Chu. From 2009 until 2015, he portrayed the role of Mike Chang, a dancer who joins the glee club, on the Fox musical comedy-drama series Glee. Known for a while as “Other Asian” on Glee, he was given very few lines during the show’s first season. Partly due to the enthusiasm from fans during his appearances on the live tour taking place after the first season concluded, Shum’s character was given storylines in the second season, mostly involving his relationship with fellow glee club member Tina Cohen-Chang (Jenna Ushkowitz). He subsequently gave performances of “Make ‘Em Laugh” in “The Substitute”, “Sing” from A Chorus Line in “Duets”, “Valerie” in “Special Education”, and the show’s first dance solo in “A Night of Neglect”. He was promoted from guest star to series regular for the third season. He was given a major storyline in the third episode of the season, “Asian F”, and performed “Cool” from West Side Story, his first solo song. On June 28, 2013, it was reported that Shum would not return as regular on Glee’s fifth season, but would be a recurring guest star.

Shum worked as both a choreographer and a dancer for the dance group The LXD. Along with Chrisopher Scott, Harry choreographed performances during the Ellen’s Even Bigger Really Big Show, the 82nd Academy Awards and So You Think You Can Dance. The LXD also worked as the opening act for the Glee Live! In Concert! tour starting in May 2010. A mini web series of the same name and starring The LXD was created by Jon M. Chu, with Shum again taking the position of the choreographer and portrayed Elliot, while also writing the script for one of the episodes.

Shum has been featured in many productions of Wong Fu Productions. In 2011, Shum worked in a short action film, 3 Minutes, directed by Ross Ching and produced by Don Le and George Wang. In 2012 he starred in White Frog, a comedy-drama film directed by Quentin Lee. Subsequently, Shum was cast in the role of the Kuai Liang (the younger Sub-Zero) in the second season of Mortal Kombat: Legacy. In 2014, he had a major role in crime drama film Revenge of the Green Dragons, which was executive produced by Martin Scorsese. Shum was also the judge on the reality competition television series Fake-Off.

In 2016, Shum appeared as the character Wei-Fang in the Netflix American–Chinese martial arts film Crouching Tiger, Hidden Dragon: Sword of Destiny, a sequel to Crouching Tiger, Hidden Dragon (1999). Shum was also cast as the male lead, Peter Ma, in Single By 30, a YouTube Red original series from Wong Fu Productions and New Form Digital after starring in the original pilot in 2015. The first season of the series premiered on August 24, 2016, on Wong Fu Productions’ Channel.

Shum scored a lead role in the Freeform series, Shadowhunters, and portrayed the centuries-old warlock Magnus Bane between 2016 and 2019. The show is based on Cassandra Clare’s best-selling young adult fantasy series, The Mortal Instruments. His portrayal of Bane, a bisexual man of color, helped Shadowhunters win the 2017 GLAAD media award for an “Outstanding Drama Series”, which he accepted with his co-star Matthew Daddario. Shum also received the Bisexual Representation Award (BiRA) for “Best Bisexual Representation of a Supporting Character” in both 2017 and 2018 hosted by FluidStyleCo. Shum won the award for The Male TV Star of 2018 in the E! People’s Choice Awards for his role as Magnus Bane in Shadowhunters.

Alongside his work in Shadowhunters, he received supporting roles in movies including Escape Plan: The Extractors and Burn. In 2018, Shum was cast as Charlie Wu in Jon M. Chu’s Crazy Rich Asians, and despite most of his scenes being cut due to the desire to focus on one romantic pairing, he appears briefly in a mid-credits scene near the end. An implied romance between Astrid and his character Charlie is to be expanded in the movie sequels currently in the work.

In 2019 Shum appeared in 4 episodes of Tell Me a Story which premiered in December 2019. In late 2019, it was announced that Shum would star in All My Life alongside Jessica Rothe, as well as the thriller movie Broadcast Signal Intrusion.