For a period in his youth, Reshevsky did not attend school, for which his parents appeared in District Court in Manhattan, facing a charge of improper guardianship.

He gave up most competitive chess for seven years, from 1924 to 1931, to complete his secondary education while successfully competing in occasional events during this period.

[11] He then won first place at the Margate tournament, where he beat, among others, former world champion José Raúl Capablanca; the game followed the Exchange Variation of the Queen's Gambit Declined.

He was one of five chess grandmasters to compete in the World Championship match tournament in The Hague/Moscow 1948 and finished in joint third place with Paul Keres, behind Mikhail Botvinnik and Vasily Smyslov.

[14] The following Candidates in Zurich 1953 tournament was probably Reshevsky's best chance to qualify for a World Championship match, but he finished in joint second place with David Bronstein and Keres, two points behind Smyslov.

Bronstein, in his last book, Secret Notes, published in 2007 just after his death the previous year, confirmed long-standing rumours by writing that the nine Soviet grandmasters (out of a field of 15 players) at Zurich were under orders from both their chess leadership and the KGB not to let Reshevsky win the tournament under any circumstances, with Smyslov being the preferred victor.

Bronstein had earlier (1995) written that he was ordered by the Soviet delegation leader to win as Black against Reshevsky in the second cycle at Zurich and managed to do so after a very hard struggle.

In 1952, New York hosted the first eight games of an informal match for "The Championship of the Free World" between Reshevsky and Polish-Argentine grandmaster Miguel Najdorf.

Reshevsky was quickly outplayed on the White side of the Queen's Gambit Accepted in the first game and eventually fell on time in a lost position.

In the second game, he played sharply with Black, but Portisch was able to exchange the queens and a pair of rooks, thus draining much of the tension in the position.

An Open Sicilian arose, but Portisch seized the initiative on the queenside; having gained a clear advantage, he was able to translate it into a crushing kingside attack, thus winning the match and the final Candidates spot.

Amsterdam 1964 was the first meeting between these two chess greats, and Portisch was to prove a difficult opponent for Reshevsky, whose lifetime score against him was (+0−4=9).

Reshevsky played on top board for the US in the 1955 team match against the USSR, held in Moscow, and defeated World Champion Mikhail Botvinnik over four games, winning one and drawing three.

Once Bobby Fischer made his debut at age 14 in the US Championship with the 1957–58 event, he dominated completely, winning on each of his eight attempts, leaving Reshevsky, the seven-time former champion, back in the chasing pack.

Reshevsky also refused to play for the US team in the Chess Olympiads of 1960, 1962 and 1966 because Fischer, as US champion, was chosen ahead of him for the top board.

This was around the time when Reshevsky defeated World Champion Mikhail Botvinnik in their four-game mini-match, which was the top board of the US vs. USSR team match held in Moscow.

He defeated seven world champions: Lasker, José Raúl Capablanca, Alexander Alekhine, Max Euwe, Mikhail Botvinnik, Vasily Smyslov, and Bobby Fischer.

Aside from US Championships, Reshevsky's important tournament titles included: Syracuse 1934, Hastings 1937–38, Leningrad/Moscow 1939, Hollywood 1945 (Pan American Championship), New York 1951 (Maurice Wertheim Memorial), Havana 1952, New York 1956 (Lessing Rosenwald Trophy), Dallas 1957, Haifa/Tel Aviv 1958, Buenos Aires 1960, Netanya 1969, Reykjavík Open 1984, at age 72.

Reshevsky's inadequate study of the opening and his related tendency to fall into time pressure may have been the reasons that, despite his great talent, he never became world champion; he himself acknowledged this in his book on chess upsets.

This shortcoming was similarly noted by GM Larry Evans in commentary contained in Fischer's book My 60 Memorable Games.

Contemporary American GM Arnold Denker complimented Reshevsky's extraordinary tenacity and fighting spirit and noted that Reshevsky developed a vital advantage in his great head-to-head battles with his main American rival, GM Reuben Fine, particularly in US Championships from the mid 1930s through the early 1940s.