Andrei Kramarevsky was born in Kharkov, Ukraine, and began his dance training at the academy of the Bolshoi Ballet at age 9. During WWII, he moved to Kirgistan and joined the local ballet theater, Frunze, when he was just 12. He rose to the rank of soloist, and in 1945 returned to Moscow to resume his training at the Moscow Ballet School, where the noted Bolshoi dancer Nikolai Tarasov was one of his formative teachers.
In 1949, Kramarevsky joined the Bolshoi Ballet, where he worked extensively with the famed Bolshoi dancer, choreographer and coach Asaf Messerer. He was promoted to principal dancer in 1959. During his 18 years with the Bolshoi, Kramarevsky performed a number of soloist and principal roles in ballets such as Swan Lake, The Nutcracker, Faust, The Bronze Horseman and The Fountains of Bakhchisarai. He accompanied the company on many world tours, dancing in London, Japan, Paris, Germany, New Zealand and beyond.
In 1967, Kramarevsky joined Moscow Concert, teaching professional classes and taking on acting, singing and dancing roles. Before leaving Moscow Concert in 1975, he had held the titles of ballet master and director.
In 1975, Kramarevsky defected to Italy and taught at dance schools in Rome and Napoli. Almost immediately upon arriving in the United States in February 1976, he was invited by the School of American Ballet's executive director to guest teach a class. The next day, George Balanchine asked Kramarevsky to guest teach a company class at New York City Ballet. Balanchine observed the class and offered him a job on the spot. Kramarevsky joined SAB's permanent faculty, and frequently taught NYCB company classes for Balanchine until the early 1980s.
In 2003, Kramarevsky was named to SAB's Mae L. Wien Faculty Chair. In addition to his regular teaching duties at SAB, he often performs character roles with New York City Ballet in George Balanchine's The Nutcracker™, The Sleeping Beauty and Harlequinade.