Ribli's first significant achievement was winning the Hungarian Junior Championship in 1968. Subsequently, he won the Hungarian Championship three times (1973, 1977 and 1983). He qualified for three Interzonals in the period of 1976-1987. His best World Championship performance came in the Candidates Tournament in 1985, where he reached the semi-final but lost against Andrei Sokolov.
Ribli's career is not limited to individual contests. He has also made significant contributions to the Hungarian team, including appearances in eight Chess Olympiads. He helped guide the team to a gold medal victory in 1978 in Buenos Aires.
Outside of his playing career, Ribli also served as an appointed FIDE vice president from 1994-1996. He made other contributions to the chess world as well, including acting as second to Anatoly Karpov during his 1986 championship match against Garry Kasparov.
Ribli has been less active as a competitor in recent years, but he remains involved in chess as a trainer and author, contributing to the popular series "Chess Informant". He also serves as a chess arbiter, or judge, at various competitions.