1959Artist of the People of the USSR
1962Anna Pavlova Prize awarded in Paris
1977City’s gold medal of Paris by mayor of Paris Jacques Chirac
1985Hero of Socialist Labour

Commander of the Order of Arts and of Letters (L’Ordre des Arts et des Lettres)
1986Order of the French Legion of Honour
1987Appointment as professor at the Sorbonne
1991Gold Medal for Servive to the Arts awarded by Spanish King Juan Carlos
1993Appointment as professor at the Lomonossov State University in Moscow
1995First Medal for Service to the Russian state (for distinguished services in the development of choreographic art)
2000Second Medal for Service to the Russian state awarded by Russian President Vladimir Putin

"Russian National Olympus Prize" in the nomination "Honorary Title: Superstar"

Winner of the Russian prize "Triumph" for the encouragement of the achievements in art and literature
2005Prince of Asturias Award for Arts (Oviedo/Spain)

Thirth Medal for Service to the Russian state awarded by Russian President Vladimir Putin

Barbora-Radvilaite-Award (Vilnius/Litvania)
2006Awarded with the prize "Praemium Imperiale" in the nomination Theatre/Film (Japan)
2008Member of the Armenian branch of the International Academy of Natural and Social Sciences

Honorary doctor at the Hungarian Dance Academy, Budapest
2009„Vittorio De Sica Award“ (Italy) „in recognition for the outstanding career in dance”

Awarding with the Russian ballet prize „Soul of the Dance“ in the category „Legend“
2010Awarding with the “Order of Merit for the Fatherland” of the fourth class by the Russian President Dmitri Medvedev for the outstanding contribution in the development of Russian culture, the Art of Ballet and the long-time artistic activity
2011Officer of the National French Order of the Legion of Honor
2013Awarded with the prize "Baltic Star"
2015"Golden Mask" for outstanding achievements in the development of Arts