Alena Baeva graduated from the TsSSMSh and the Moscow State Tchaikovsky Conservatory (class of Prof. Eduard Grach). At the invitation of Mstislav Rostropovich, she trained in France. Participated in master classes with Ida Handel, Shlomo Mintz, Boris Garlitsky and Maxim Vengerov.

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Winner of the international competitions for violinists named after G. Wieniawski in Poznań, named after N.  Paganini in Moscow (Grand Prix) and the competition in Sendai (Japan). Winner of the youth award "Triumph" (2007). Since 2009 he has been collaborating with the Orpheum Foundation (Switzerland).

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She has performed in prestigious concert halls with leading orchestras of the world conducted by V. Gergiev, N. Marriner, P. Berglund, V.  Fedoseeva A.  Lazareva, P. Gulke, V. Spivakova, J.-K. Casadesus, S. Oramo, K. Yamada. Among the chamber ensemble partners are Y. Bashmet, E. Virsaladze, A. Knyazev, A. Rudin, K. Skanavi, I. Golan, V. Kholodenko, Sh. Vladar. In 2014 she organized a string quartet.

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Participated in the festivals "December Evenings", "Stars of the White Nights", "Virtuosi of the 21st Century" (New York), "Academy of Seiji Ozawa" (Switzerland), "Violin at the Louvre" and Juventus (France), "Ravinia" (Chicago ), "Return" (Moscow), festivals in Menton, Vienna, Athens, Istanbul, Brazil, etc. Participated in the largest open-air concert in Europe (120,000 listeners) in Nuremberg broadcast on the Bavarian radio.

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The artist has made a number of stock recordings on radio and television in Belgium, Germany, Poland, Portugal, Israel, Japan, Russia and the USA. She has recorded a number of CDs for Pentatone Classics, DUX, SIMC, fontec, Arthaus Musik. Alena Baeva's concerts were broadcast by the Kultura, TV Center, Mezzo, Arte TV channels, as well as BBC radio.