[7] Adams' early endeavours were already beginning to pay dividends at the British Championship of 1987, where he gained his final IM norm and took the best junior prize.

In 1993 he finished equal first (with Viswanathan Anand) in the Groningen Interzonal tournament to determine challengers for the PCA World Chess Championship 1995.

In 1997, he took part in the 1997–1998 FIDE World Championship, which, for the first time, was a large knockout event, the winner of which would play a match against reigning champion Anatoly Karpov.

This tournament included most of the world's top players (Garry Kasparov, Vladimir Kramnik, and Gata Kamsky were the only notable absentees), and Adams won short matches against Tamaz Giorgadze, Sergei Tiviakov, Peter Svidler, Loek van Wely and Nigel Short, before coming up against Anand in the final round.

[13] Adams came closest to claiming a world title at the 2004 FIDE Championship when he reached the final, winning matches against Hussein Asabri, Karen Asrian, Hichem Hamdouchi, Hikaru Nakamura, Vladimir Akopian and Teimour Radjabov.

Among his other notable results were first place at Terrassa in 1991, joint first at Dos Hermanas in 1995 (with Kamsky and Karpov), joint first at Dortmund Sparkassen Chess Meeting in 1998 (with Kramnik and Svidler) and clear first at Dos Hermanas in 1999, ahead of Kramnik, Anand, Svidler, Karpov, Veselin Topalov, Judit Polgár and others.

In more recent times, he won the fifth Howard Staunton Memorial Tournament[14] in August 2007, achieving a score of 8½/11 (six wins, five draws), picking up the top purse of £1000.

[15] Prior to the start of the tournament, on 4 August, Adams married his longtime girlfriend, the actress Tara MacGowran, at a ceremony in Taunton, close to where they live.

[17] Adams won the 2nd Ruy Lopez Masters tournament held in Mérida, Spain, 4–13 April 2008, scoring 5½/7 to finish a half-point ahead of Zhang Pengxiang.

[20] He followed this with a share of second place at the 4th EU Individual Open Chess Championship in Liverpool, joining Viktor Láznička and Nigel Short on 7½/10 (after winner Jan Werle, 8/10).

Adams finished outright first at the Los Angeles Metropolitan International and the European Team Championship and was awarded the gold medal for his performance on board one.

He won the tournament with five wins and four draws (7/9), ahead of a field of 9 other grandmasters whose ratings averaged over 2705, including Fabiano Caruana (2796) and Vladimir Kramnik (2784).

[25] In October of that year, the sixth Grand Slam Chess Masters final was held in Bilbao as a double round-robin with four players.

[26] 2014 included two notable results; a silver medal for his performance on board 1 at the Tromsø Olympiad and a share of first place at the London Chess Classic Blitz tournament (with Nakamura and Kramnik).

[27] Hydra, housed in Abu Dhabi at the time of the match, consisted of 64 PCs, each running 3.06 GHz Intel Xeon processors.