Aleksei Evgrafovich Favorskii was an outstanding organic chemist who left a great scientific legacy as a result of his long and fruitful research. Most of theoretically and practically important discoveries made by A.E.Favorskii lay in the area of acetylene chemistry. Nowadays the reactions he discovered, namely, acetylene--allene isomerization, Favorskii reaction, retro-Favorskii reaction, Favorskii rearrangement and vinylation are widely used in industry and in laboratory organic synthesis. This review summarizes the key scientific achievements of A.E.Favorskii and describes further development of these areas in modern organic synthesis. Detailed consideration is given for the acetylene--allene isomerization and `acetylene zipper' reaction as convenient synthetic tools for the synthesis of methyl-substituted acetylenes and acetylenes with a terminal triple bond, respectively. The review presents examples of the use of these reactions in the modern organic synthesis of complex molecules, including natural co