quality:correction
1945–1990: Post-World War II era

After the death of Alekhine, a new World Champion was sought. FIDE, which has controlled the title since then, ran a tournament of elite players. The winner of the 1948 tournament was Russian Mikhail Botvinnik. In 1950, FIDE established a system of titles, conferring the title of Grandmaster on 27 players. (Some sources state that, in 1914, the title of chess Grandmaster was first formally conferred by Tsar Nicholas II of Russia to Lasker, Capablanca, Alekhine, Tarrasch, and Marshall, but this is a disputed claim.)

Botvinnik started an era of Soviet dominance in the chess world, which mainly through the Soviet government's politically inspired efforts to demonstrate intellectual superiority over the West stood almost uninterrupted for more than a half-century. Until the dissolution of the Soviet Union, there was only one non-Soviet champion, American Bobby Fischer (champion 1972–1975). Botvinnik also revolutionized opening theory. Previously, Black strove for equality, attempting to neutralize White's first-move advantage. As Black, Botvinnik strove for the initiative from the beginning. In the previous informal system of World Championships, the current champion decided which challenger he would play for the title and the challenger was forced to seek sponsors for the match. FIDE set up a new system of qualifying tournaments and matches. The world's strongest players were seeded into Interzonal tournaments, where they were joined by players who had qualified from Zonal tournaments. The leading finishers in these Interzonals would go through the " Candidates " stage, which was initially a tournament, and later a series of knockout matches. The winner of the Candidates would then play the reigning champion for the title. A champion defeated in a match had a right to play a rematch a year later. This system operated on a three-year cycle. Botvinnik participated in championship matches over a period of fifteen years. He won the world championship tournament in 1948 and retained the title in tied matches in 1951 and 1954. In 1957, he lost to Vasily Smyslov, but regained the title in a rematch in 1958. In 1960, he lost the title to the 23-year-old Latvian prodigy Mikhail Tal, an accomplished tactician and attacking player who is widely regarded as one of the most creative players ever, hence his nickname "the magician from Riga". Botvinnik again regained the title in a rematch in 1961.

Following the 1961 event, FIDE abolished the automatic right of a deposed champion to a rematch, and the next champion, Armenian Tigran Petrosian, a player renowned for his defensive and positional skills, held the title for two cycles, 1963–1969. His successor, Boris Spassky from Russia (champion 1969–1972), won games in both positional and sharp tactical style. The next championship, the so-called Match of the Century, saw the first non-Soviet challenger since World War II, American Bobby Fischer. Fischer defeated his opponents in the Candidates matches by unheard-of margins, and convincingly defeated Spassky for the world championship. The match was followed closely by news media of the day, leading to a surge in popularity for chess; it also held significant political importance at the height of the Cold War, with the match being seen by both sides as a microcosm of the conflict between East and West. In 1975, however, Fischer refused to defend his title against Soviet Anatoly Karpov when he was unable to reach agreement on conditions with FIDE, and Karpov obtained the title by default. Fischer modernized many aspects of chess, especially by extensively preparing openings.

Karpov defended his title twice against Viktor Korchnoi and dominated the 1970s and early 1980s with a string of tournament successes. In the 1984 World Chess Championship, Karpov faced his toughest challenge to date, the young Garry Kasparov from Baku, Soviet Azerbaijan. The match was aborted in controversial circumstances after 5 months and 48 games with Karpov leading by 5 wins to 3, but evidently exhausted; many commentators believed Kasparov, who had won the last two games, would have won the match had it continued. Kasparov won the 1985 rematch. Kasparov and Karpov contested three further closely fought matches in 1986, 1987 and 1990, Kasparov winning them all. Kasparov became the dominant figure of world chess from the mid-1980s until his retirement from competition in 2005.