Azari Plissetski studied music at the Central School of Music of the Moscow conservatory, and then at twelve, devoted himself to dance at the Bolshoi Ballet Academy. He began his career as dancer, in 1957, at the Bolshoi before receiving, five years later, the offer of joining the Ballet National de Cuba. From 1963 to 1973, Azari Plissetki taught, set ballets, and performed the lead roles in the company. With his principal partner, dancer Alicia Alonso, he participated in the creation of the new school for the Ballet National de Cuba, who progressively gained an international reputation.
Back with the Bolshoi in 1973, where he continued his dance career until 1978, and was also guest teacher for two years for Roland Petit’s company. From 1978 to 1981, Maurice Béjart hired him as teacher for the Mudra School and the Ballet du XXe Siècle in Brussels. After this, Azari became teacher for the Moscow Classical Ballet until 1984. From 1984 to 1987, he was invited by Roland Petit to teach for his company and at the Stuttgart Ballett to set numerous works. In 1987, he joined his sister, the famous dancer Maya Plissetskaya, who was at the time director of the National Ballet of Madrid.
Since 1991, he is teacher at the Béjart Ballet Lausanne and the Rudra Béjart Ballet Lausanne. He is regularly invited to teach at prestigious international companies, including the Kirov, Mariinsky, Mikhailovski and the Bolshoi in Russia, as well as the Baryshnikov Arts Center, the New York City Ballet and the American Ballet Theatre in the USA. His choreographic works continue also with the Japanese company Asami Maki Ballet for which he choreographed numerous works: Don Quixote, Romeo and Juliet and La dame aux camélias.