Tall fast bowler Alzarri Joseph started out as a legspinner in his backyard in Antigua before his height marked him out for a different style of bowling. In his teens he gained a reputation as one of the fastest bowlers on the school circuit, which carried over into the 2016 Under-19 World Cup, where he bowled the competition's fastest delivery, a 147kph zinger that broke Zimbabwe batter Brendan Sly's stumps. Joseph would finish as West Indies' highest wicket-taker of the tournament, with 13 wickets from six games at an economy of 3.31.

He had made it into the U-19 World Cup squad on the back of his first-class performances - in his second season with Leeward Islands in late 2015, he took his first five-for, against Guyana, and followed it up with 7 for 46 against Windward Islands in the next match. His 24 first-class wickets that season and the World Cup performance saw him fast-tracked into the Test side; he debuted against India at Gros Islet in August 2016 and bounced out Virat Kohli for 3 for his first wicket. His ODI debut came a few months later, against Pakistan in Sharjah.

In 2019, Joseph was signed by Mumbai Indians as an injury replacement for Adam Milne, and in his first game, against Sunrisers Hyderabad, he returned figures of 6 for 12, the best figures by a bowler in the IPL.