Criville started his international career in the now-defunct 80cc World Championship, taking a 2nd place in his very first race in 1987. He was 7th overall in 1988, also dabbling in the 125cc series, which he raced fulltime in 1989. He won the 125cc World Championship in his first attempt riding for the JJ Cobas team, claiming 5 victories.
In 1990 he stepped up to the 250cc class for Giacomo Agostini's team, before returning to the Cobas team a year later, without having won a 250cc race.
Nonetheless, Alex joined the Sito Pons team in 500cc for 1992, taking 8th overall, and his first win at Assen. In 1993, he again finished 8th in the championship. 1994 was his first year as a full factory Honda rider, as Mick Doohan's team-mate on the Repsol-backed Hondas which would dominate 500cc and MotoGP racing in years to come. Alex was 4th in 1995 and 1997, runner-up in 1996 with 11 podium finishes, and 3rd in 1998.
Doohan's career-ending crash in 1999 opened the door for Criville, and he took six wins, including his 100th 500cc start at Donington Park , clinching the championship with a race to spare. However, he finished 9th in 2000 and 8th in 2001. Fired by Repsol Honda, he planned to spend the 2002 MotoGP season with the D'Antin Yamaha team, but was forced to retire due to medical problems, having started to suffer symptoms related to epilepsy as a result of previous crashes.