As one of the top prospects in the country, Martin was selected as a McDonald's All-American, the first for LSU head coach Johnny Jones.

[2] On March 25, 2015, Martin declared for the NBA draft, forgoing his final two years of college eligibility.

[11] On October 30, 2016, Martin made his first career start,[12] recording four points and five rebounds in 19 minutes in a 112–103 overtime win over the Washington Wizards.

He scored in double figures 23 times, including a career-high 20 points on December 27 against the Los Angeles Lakers.

He pulled down 10+ rebounds five times, including a career-high 14 boards on March 28 against the Portland Trail Blazers, and recorded two double-doubles.

[16] On July 23, 2018, Martin and cash considerations were traded to the Orlando Magic in exchange for Dakari Johnson and the draft rights to Tyler Harvey.

[19] On December 5, 2019, Martin joined the Shenzhen Aviators of the Chinese Basketball Association (CBA) to replace Shabazz Muhammad.

[16] On December 2, 2020, Martin signed a one-season (plus option) contract with the Sydney Kings of the Australian National Basketball League (NBL).

[24] On July 4, 2022, Martin signed a two-year deal with Maccabi Tel Aviv of the Israeli Premier League.

[28] In December 2023, he suffered a patellar tendon rupture in his right knee during a round 11 BSL game.

[30] Having recovered from his patellar tendon injury, but dealt with a foot complaint during the pre-season that ruled him out until November 2024.