In 1969–70, Adorján secured the title of European Junior Champion at the 'Niemeyer Tournament' in Groningen, and in 1969 at Stockholm, he finished runner-up in the World Junior Chess Championship to Anatoly Karpov. Qualification as an International Master came in 1970 and as a Grandmaster in 1973. The latter was also the year that he won (jointly) his first Hungarian Championship, going on to a further (this time outright) victory in 1984.

Other tournament successes (finishing either first or joint first) included Varna 1972, Osijek 1978, Budapest 1982, Gjovik 1983, Esbjerg 1985 and New York Open 1987. In an interview, he recounts the story of his telephoned invitation to Luhacovice in 1973; he enquired—"Is there a GM norm on offer?", to which came the answer "Yes". His next question—"When does it start?" was met with the reply "Half an hour ago". He also went on to win that tournament. At the Riga Interzonal of 1979, he finished joint third and qualified for the World Championship Candidates Tournament via tiebreaks, after drawing a match (+1 −1 =2) with fellow Hungarian Zoltán Ribli. At the Candidates he lost his quarter-final match to Robert Hübner.

In team chess, Adorján has an excellent record. Competing at the Chess Olympiad of 1978, he helped Hungary to capture the gold medal from the Soviet team who had convincingly won the event twelve consecutive times from 1952 through 1974. His further participation in 1984, 1986 and 1988 contributed to a top five finish on each occasion. Compatriots Lajos Portisch, Ribli and Gyula Sax were also at the peak of their playing strength during this period.

Adorján has also worked over the years, sometimes secretly, as a second to Garry Kasparov and to Peter Leko, helping them to prepare for important World Championship matches. He is known as a leading expert on the Grünfeld Defence, which has been favored by both Kasparov and Leko.

Adorjan is also an International Arbiter (1994).

Wikipedia article: András Adorján