Beliavsky played on the top board for the USSR team that won the gold medal in the 1984 Chess Olympiad.

At the second Russia (USSR) vs Rest of the World match in 1984, he was the top scorer for the victorious Soviet team, defeating Yasser Seirawan 2–0 and Bent Larsen 1½–½.

[5] From September 2009 to May 2010, he was the oldest person among the world's top 100 active players,[6][7][8][9][10] and he made a brief reappearance in June 2013 at age 59.

[12] In 2013 he tied for 1st–8th places with Alexander Moiseenko, Evgeny Romanov, Hrant Melkumyan, Constantin Lupulescu, Francisco Vallejo Pons, Sergei Movsesian, Ian Nepomniachtchi, Alexey Dreev and Evgeny Alekseev in the European Individual Chess Championship, thus qualifying for the FIDE World Cup.

He has defeated nine - every undisputed world champion from Vassily Smyslov to Magnus Carlsen except Bobby Fischer - a record he shares with Paul Keres and Victor Korchnoi.