Martin, who grew up in Miami, Florida, is the son of Cuban political exiles and the first American-born member of his family. He graduated with a bachelor's degree in physical education from Florida International University in 1993. One of the two jobs he held while attending FIU was that of a bouncer at a local nightclub. He decided to become a full-time basketball coach in 1992 as a result of an incident in which he was subjected to gunfire, while on duty, from a group of men whom he had ejected for fighting.
At the same time, he had begun his career in basketball as the head coach of the boys' junior varsity squad at Miami High School in 1985. He served in that position for eight years until he was appointed to his first varsity coaching job at North Miami High School after he completed his studies at FIU in 1993. He returned to Miami Senior two years later to head its varsity team. Under his watch, the Stingarees won three consecutive state championships from 1996 to 1998 with teams featuring future NBA players Udonis Haslem and Steve Blake. The last of those titles was later vacated due to recruiting violations involving school employees and boosters who gave housing assistance to the players. Although he was never personally accused of any wrongdoing, Martin was dismissed in 1999. He next served as head coach at Booker T. Washington High School for one year.
Martin joined the college ranks as an assistant coach/recruiting coordinator at Northeastern University from 2000 to 2004. He moved to the University of Cincinnati, serving one season each under Bob Huggins and Andy Kennedy. Martin followed Huggins to Kansas State, joining his staff on April 5, 2006. On April 6, 2007, almost a year to the day after his arrival in Manhattan, Martin was named head coach of the Wildcats in the wake of Huggins' resignation.
Martin's first season as head coach at Kansas State was marked by a number of noteworthy events. The 2007–2008 Wildcats, featuring star freshman Michael Beasley, were included in the preseason Top 25 for the first time since 1972. On January 19, 2008, Martin's Wildcats defeated then-No. 10 Texas A&M, giving the team its first win over a ranked team in nearly a year, and its first victory over a Top 10 team since beating Texas in March 2004. On January 30, 2008, Martin led Kansas State to an 84–75 victory over then-No. 2 Kansas, marking the Wildcats' first home win over their in-state rival since 1983. Ultimately, Martin led Kansas State to its first berth in the NCAA Tournament since 1996.
Martin was awarded the Big 12 Conference Coach of the Year by the conference on March 7, 2010. Later that month, he led the Wildcats to the Elite 8, their best tournament performance since 1988.
He was given a contract extension through the 2014-2015 season. His salary increased to $1.2 million, plus incentives, for 2010-11. The salary would increase by $100,000 a year for each subsequent year of the contract, topping out at $1.6 million in 2014-15.
After Frank Haith left Miami to take the Missouri head coaching job in the spring of 2011, there were rumors that Martin, born and raised in Miami, might leave Kansas State to take the job. These rumors ended when it was announced that Jim Larranaga took the job at Miami.
On March 26, 2012, in a text message to ESPN, Martin confirmed he had accepted the head coach position at South Carolina. On March 27, 2012, Martin was introduced as South Carolina's head coach, replacing Darrin Horn.
Martin posted losing records in each of his first two seasons at South Carolina, including a combined conference mark of 9–27. His team's most notable victory in those two seasons was a 72–67 home win against #17 Kentucky on March 1, 2014. During the 2013–14 season, Martin issued a public apology to fans and players on January 21, 2014, after a verbal tirade during the team's loss to Ole Miss. On March 6, 2014, USC Athletic Director Ray Tanner suspended Martin for the final game of the regular season for further "inappropriate verbal communication" with players.
In Martin's third season at South Carolina, he recorded his first winning season at South Carolina with a 17–16 (6–12) record. The team posted a 9–3 record in its non-conference season, concluding with a win over #9 Iowa State at the Brooklyn Hoops Showcase, and followed this by finishing its SEC conference regular season with a 6–12 record, then posting a 2–1 mark in the SEC Tournament.
The 2015–16 season continued the upward trend as his Gamecocks won 24 regular season games, including a spotless 15–0 mark in the non-conference. The 11–7 mark in conference was good enough to tie for third in the SEC, but after losing to Georgia in the SEC Tournament, South Carolina accepted an NIT bid.
The 2016-17 team finally broke through and earned a bid as a #7 seed to the 2017 NCAA Tournament, where they earned their first win in the event since 1973 with a 20-point victory over the #10 seed Marquette Golden Eagles, followed by a win over #2 seed Duke advancing to the program's first Sweet 16 in school history. The Gamecocks then beat Baylor to go onto the Elite 8 for the first time in school history. On Sunday, March 26, 2017, South Carolina defeated Florida in the East Regional Final to reach the school's first ever Final Four. They played Gonzaga on April 1, 2017 and lost 73 to 77, ending their road to a national championship.