In a 1920 tournament in Berlin, he finished first (+6−2=1) ahead of Efim Bogoljubov, Savielly Tartakower, Richard Réti, Géza Maróczy, and Siegbert Tarrasch.

In 1921, Breyer set a new blindfold chess record by playing 25 games simultaneously.

He also edited Szellemi Sport, a magazine devoted to chess puzzles, and composed at least one brilliant retrograde analysis study.

Breyer was a leading pioneer of the hypermodern school of chess theory, which favoured controlling the centre with pressure from the flanks.

[1] He is most notably recognised for the Breyer Variation in the Ruy Lopez, which involves Black re-routing his queen's knight to d7 for increased flexibility (1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 Be7 6.Re1 b5 7.Bb3 0-0 8.c3 d6 9.h3 Nb8 10.d4 Nbd7; see diagram).