Reshevsky learned to play chess at age four, and was soon acclaimed as a child prodigy. At age eight he was beating accomplished players with ease, and giving simultaneous exhibitions. In November 1920, his parents moved to the USA to make a living exhibiting their child. He played in the 1922 New York Masters tournament.

As an adult, however, Reshevsky was never a professional chess player. He temporarily gave up chess to enter the University of Chicago, graduating in 1934 with a degree in accounting. He supported himself and his family by working as an accountant. His 1941 marriage to the former Norma Mindick produced three children.

Reshevsky was a devout Orthodox Jew and did not play on the Jewish Sabbath, with his games scheduled accordingly.

Reshevsky won the U.S. Chess Championship in 1936, 1938, 1940, 1941, 1942, 1946, and 1969. As well, Reshevsky tied for that tournament title in 1972, but lost the playoff in 1973 to Robert Byrne. He competed in a record 21 U.S. Championships, and achieved a plus score every time. He also holds U.S. Championship records for most finishes in the top three places (15), most games played (269), and most games won (127).

He won the U.S. Open Chess Championship in 1931 at Tulsa. Nice 1931 Reshevsky shared the 1934 U.S. Open title with Reuben Fine at Chicago. GER-ch 2nd Aachen 1934 Reshevsky's international career began in 1935 with a trip to England, where he won at Yarmouth with 10/11. He then won first place at the Margate tournament where he beat, among others, former world champion José Raúl Capablanca. The game transcript follows. Reshevsky has the white pieces:

1. d4 Nf6 2. c4 e6 3. Nc3 d5 4. Bg5 Nbd7 5. cxd5 exd5 6. e3 Be7 7. Bd3 O-O 8. Qc2 c5 9. Nf3 c4 10. Bf5 Re8 11. O-O g6 12. Bh3 Nf8 13. Bxc8 Rxc8 14. Bxf6 Bxf6 15. b3 Qa5 16. b4 Qd8 17. Qa4 a6 18. b5 Re6 19. Rab1 Rb8 20. Rb2 Be7 21. bxa6 Rxa6 22. Qc2 Ne6 23. Rfb1 Ra7 24. a4 Nc7 25. Ne5 Qe8 26. f4 f6 27. Ng4 Qd7 28. h3 Kg7 29. Nf2 Ba3 30. Ra2 Bd6 31. Nfd1 f5 32. Nb5 Ra5 33. Nxc7 Bxc7 34. Nc3 Qd6 35. Qf2 b6 36. Qf3 Rd8 37. Rab2 Qe7 38. Rb4 Rd7 39. Kh1 Bd8 40. g4 fxg4 41. hxg4 Qd6 42. Kg1 Bc7 43. Kf2 Rf7 44. g5 Bd8 45. Ke2 Bxg5 46. Rxb6 Qa3 47. Kd2 Be7 48. Rb7 Rxa4 49. Qxd5 Ra5 50. Qxc4 Rh5 51. Kd3 Qa8 52. Qe6 Qa3 53. Rd7 Rhf5 54. Rb3 Qa1 55. Rxe7 Qf1+ 56. Kd2 1-0

A year later he shared third place at the Nottingham 1936 chess tournament. In 1937 he shared first at Kemeri, Latvia, and in 1938 shared fourth in the AVRO tournament in the Netherlands, which featured arguably the eight strongest players in the world. Reshevsky won his third U.S. Open title at Boston 1944.

Reshevsky was a serious contender for the World Championship from roughly 1935 to the mid-1960s. He was one of the 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.

In 1950, Reshevsky was awarded the title of International Grandmaster by FIDE, the World Chess Federation, on its inaugural list. Although eligible, he did not play in the Candidates Tournament in Budapest. It has generally been believed that he was barred from attending by the U.S. State Department due to the Cold War, and this is consistent with the fact that the only other eligible active player from a NATO country, Max Euwe of the Netherlands, also did not play. In 1991, however, Reshevsky said the decision not to go was his.

The following Candidates in Zurich 1953 was probably his 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) at Zurich were under orders from both their chess leadership and the KGB to not let Reshevsky win the tournament under any circumstances, with Smyslov being the preferred victor. When Reshevsky maintained his strong contention late into the two-month event, Bronstein claims that the Soviets prearranged several results in games amongst themselves to successfully prevent Reshevsky's overall victory, while also ensuring that Reshevsky faced the maximum test in his own games against the Soviet players. Several other writers, including Alexei Suetin (who was the second of Tigran Petrosian at Zurich 1953), also confirmed the Soviet collusion in Zurich.

Reshevsky qualified for one more Candidates', in 1967, but lost the subsequent quarterfinal to Viktor Korchnoi the following year.

He was a regular top board for the USA at the Chess Olympiads. Overall he played in eight events, helping the U.S. team to win the gold in 1937 and bronze in 1974, and winning an individual bronze medal for his performance on board one in 1950. His complete results were (+39 =49 -12) in 100 games, for 63.5 percent; he appeared on board one for the United States six times. He played in 1937, 1950, 1952, 1958, 1964, 1968, 1970, and 1974, a 37-year span.

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. An additional five games were played in Mexico City and five more in San Salvador. Reshevsky won the match, 11—7. The following year a rematch took place in Buenos Aires. Reshevsky again won, 9½—8½.

In his long career, Reshevsky proved a formidable match player. In 1941, he defeated I.A. Horowitz in a U.S. Championship playoff match by (+3 =13 -0). In 1942, he defeated Isaac Kashdan by (+6 =3 -2). In 1952, he defeated Svetozar Gligori? by (+2 =7 -1). In 1956, he defeated William Lombardy by (+1 =5 -0). In 1957, he defeated Arthur Bisguier by (+4 =4 -2). In 1957, he defeated Donald Byrne by (+7 =0 -3). In 1960, he defeated Pal Benko by (+3 =5 -2). Only in 1968, in his 57th year, did he finally lose a match, to Viktor Korchnoi, in Amsterdam in the first round of the Candidates.

Reshevsky played on top board for the USA 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.

In 1961 in New York and Los Angeles, Reshevsky began a 16-game match with the then-current U.S. Champion Bobby Fischer. Despite Fischer's recent meteoric rise, consensus opinion favored Reshevsky. After eleven games and a tie score (two wins apiece with seven draws) the match ended due to a dispute between Fischer and match organizer Jacqueline Piatigorsky, with Reshevsky receiving the winner's share of the prize fund. There was little love lost between the two players. Ahead of the Buenos Aires 1960 tournament, Reshevsky reportedly said, "I would settle for 19th place - if Fischer placed 20th." In the 1967 Sousse Interzonal, Fischer turned up 53 minutes late for his game with Reshevsky and made his opening move without a word of apology. Reshevsky, who had been convinced that Fischer had withdrawn from the tournament, lost the game badly and complained furiously to the organisers. He also refused to play for the US team in the Chess Olympiads of 1960, 1962 and 1966 because Fischer was chosen ahead of him for the top board. He did, however, play on a lower board in 1970, the only time the two men appeared in the same team.

During his long chess career, Reshevsky played eleven of the first twelve World Champions, from Emanuel Lasker to Anatoly Karpov, the only player to do so (he met Garry Kasparov but never played him). He defeated seven World Champions: Lasker, Jose Raul Capablanca, Alexander Alekhine, Max Euwe, Mikhail Botvinnik, Vasily Smyslov, and Bobby Fischer.

Aside from U.S. 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, and the Reykjavík Open 1984 at age 72.

Reshevsky competed seriously at least semi-regularly, virtually until his death in 1992. He defeated old rival Vasily Smyslov in a tournament game in 1991.

Reshevsky's books include Reshevsky on Chess (1948), How Chess Games Are Won (1962), Great Chess Upsets (1976), and The Art of Positional Play (1978). He also wrote a book on the 1972 World Championship match between his great rival Bobby Fischer and Boris Spassky. As well, he authored columns in chess magazines and The New York Times.

Reshevsky was a tough and forceful player who was superb at positional play, but could also play brilliant tactical chess when warranted. He used huge amounts of time in the opening, a dangerous tactic which sometimes forced him to play the rest of the game in a very short amount of time. That sometimes unsettled Reshevsky's opponents but at other times resulted in blunders on his part. 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 was never able to become world champion; he himself acknowledged this in his book on chess upsets.

• "By playing slowly during the early phases of a game I am able to grasp the basic requirements of each position. Then, despite being in time pressure, I have no difficulty in finding the best continuation. Incidentally, it is an odd fact that more often than not it is my opponent who gets the jitters when I am compelled to make these hurried moves."

• His self-description, "My style is somewhere between that of Tal and Petrosian", is sometimes circulated as an ironic comment (given that these two players are considered to represent opposite extremes of style) but makes more sense in its full context; from his book Great Chess Upsets: "I am essentially a positional player, although I can conduct an assault with precision and vigor, when the opportunity arises. My style lies between that of Tal and Petrosian. It is neither over-aggressive nor too passive. My strength consists of a fighting spirit, a great desire to win, and a stubborn defense whenever in trouble. I rarely become discouraged in an inferior situation, and I fear no one."