As one of the top prospects in the country, Martin was selected as a McDonald's All-American, the first for LSU head coachJohnny Jones. Martin was also the winner of the 2013 Mr. Basketball award given annually by the Louisiana Sports Writers Association to the top player in the state of Louisiana. Considered a five-star recruit by ESPN.com, Martin was listed as the No. 3 power forward and the No. 11 player in the nation in 2013.
College career
Freshman season
Martin started 25 of LSU's 34 games and averaged 10.3 points, 4.6 rebounds and 26.2 minutes per game. He ranked ninth in the SEC among freshmen in scoring, and seventh among SEC freshmen in rebounding. He averaged 11.4 points per game in SEC action with 12 of his 18 double figure scoring games coming in SEC play. For his performance, Martin was selected to the SEC All-Freshman Team.
Sophomore season
As a sophomore, Martin led LSU with 16.9 points per game and increased his rebounding to 9.2 per game. He had a career-high 28 points against Florida on February 21. He had 15 double-doubles and helped lead the Tigers to the NCAA Tournament. On March 25, 2015, Martin declared for the NBA draft, forgoing his final two years of college eligibility.
On June 25, 2015, Martin was selected with the 25th overall pick in the 2015 NBA draft by the Memphis Grizzlies. Four days later, he revealed that a stress fracture in his foot would prevent him from playing in the Summer League. Despite the injury, he signed his rookie scale contract with the Grizzlies on July 10. Less than two months later, Martin sustained another foot injury, this time fracturing his left foot after colliding with another player during a workout. On December 18, he made his NBA debut in the Grizzlies' 97–88 loss to the Dallas Mavericks. His minutes increased post All-Star break thanks to multiple injured teammates. Having scored eight points total in his NBA career up until March 7, 2016, Martin had 15 of his career-high 16 points in the first half of the Grizzlies' 116–96 loss to the Boston Celtics on March 9. During his rookie season, he had multiple assignments to the Iowa Energy, the Grizzlies' D-League affiliate. On October 30, 2016, Martin made his first career start, recording four points and five rebounds in 19 minutes in a 112–103 overtime win over the Washington Wizards. On November 28, 2016, he posted his first career double-double with 11 points and 12 rebounds in a 104–85 loss to the Charlotte Hornets. During the 2016–17 season, he had multiple assignments to the Iowa Energy.