Although none of the primary exponents of the Hypermodern School ever achieved the title of World Chess Champion, they were among the world's strongest players. World Champion Alexander Alekhine was associated with hypermodernism though his style was more of a blend with the Classical School. In practice hypermodernism has not replaced the classical theory of Steinitz and Tarrasch. Instead, modern chess textbooks describe hypermodernism as an addition, or extension, to classical theory.
Hypermodern openings include the Réti Opening, King's Indian Defence, Queen's Indian Defence, Nimzo-Indian Defence, Grünfeld Defence, Bogo-Indian Defence, Old Indian Defence, Catalan Opening, King's Indian Attack, Alekhine's Defence, Modern Defence, Pirc Defence, Larsen's opening, and to a lesser degree the English Opening. Openings such as 1.a3 do not constitute hypermodern openings since, although they delay the occupation of the centre with pawns, they also delay development which is not consistent with Hypermodernism.
Their ideas were thus a challenge to the existing orthodoxy popularised by Tarrasch in the 1890s. This orthodoxy was a rather dogmatic distillation of the ideas worked out by the great chess pioneer Wilhelm Steinitz. Steinitz was the first player who in his play demonstrated a mastery of positional chess ideas and the ideas he developed came to be known as the "Classical" or "Modern" school of thought. This school of thought emphasized the importance of "static" advantages such as: avoidance of pawn weaknesses, strong outposts for knights, and striving for "good" rather than "bad" bishops in locked pawn positions. This school of thought was in turn a reaction to the earlier swashbuckling style of Adolf Anderssen, Henry Blackburne and others who represented the Romantic school.
In 1922, Richard Réti published Die neuen Ideen im Schachspiel (the English translation, Modern Ideas in Chess, was published in 1923), an examination of the evolution of chess thinking from the time of Paul Morphy through the beginning of the hypermodern school. Tartakower's book Die hypermoderne Schachpartie (Hyper-modernist chess play) was published in 1924. Nimzowitsch's famous book Mein System (My System) was published in 1924 and included elements of Hypermodernism, but was largely a text on positional chess.