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Most grandmasters have largely abandoned the Italian Game in favour of the Ruy Lopez (3.Bb5) and Scotch (3.d4), considering those two openings better tries for a long-term advantage, but the Italian is still popular in correspondence chess, where players are allowed access to published theory, and in games between amateurs.
His name is attached to the Moeller Attack in the Giuoco Piano (1.e4 e5 2.Nf3 Nc6 3. Bc4 Bc5 4.c3 Nf6 5.d4 ed4 6.cd4 Bb4+ 7.Nc3 Nxe4 8.O–O Bxc3 9.d5) and the Moeller Defense in the Ruy Lopez (1.e4 e5 2.Nf3 Nc6 3. Bb5 a6 4.Ba4 Nf6 5.O–O Bc5).
Chigorin has several chess openings or variations of openings named after him, the two most important being the Chigorin Variation of the Ruy Lopez (1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.O-O Be7 6.Re1 b5 7.Bb3 d6 8.c3 O-O 9.h3 Na5 10.Bc2 c5 11.d4 Qc7) and the Chigorin Defence to the Queen's Gambit (1.d4 d5 2.c4 Nc6).
Black's most common reply is 2...Nc6, which usually leads to the Ruy Lopez (3.Bb5), Italian Game (3.Bc4), or Scotch Game (3.d4), though 3.Nc3 Nf6 (the Four Knights Game), often played in the late 19th to early 20th century, or, less commonly, 3....g6, (the Three Knights Game), are other possibilities.
The opening is now considered inferior to 3.Bb5, the Ruy Lopez, and 3.Bc4, the Italian Game, and is accordingly rarely seen today at any level of play.
In contrast to the Ruy Lopez (1.e4 e5 2.Nf3 Nc6 3.Bb5), by delaying Nf3, White leaves the f-pawn free to move and retains the possibility of playing f2–f4.
Steinitz Defense Doubly Deferred to the Ruy Lopez: 1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 d6 (also called the Russian Defence)