Tatjana Vassilieva has received scholarships and awards at numerous international competitions. In 1994, at the age of seventeen, she was awarded second prize at the ARD Competition in Munich, as well as the Bunkamura Orchard Hall Award, which included a concert tour of Japan. In 1999 she won first prize at the Third Adam International Cello Competition in New Zealand. At the International Izuminomori Competition Osaka, in May 2001, she won first prize as well as the Grand Prix and the Audience Prize. In October 2001 at the Seventh Concours de Violoncelle Rostropovich in Paris she was awarded, unanimously by the jury, the First Grand Prix de la Ville de Paris.
As a chamber musician Tatjana Vassilieva has performed at major international festivals with fellow musicians that include Tatjana Geringas, Cyprien Katsaris, Yuri Bashmet and Eugene Istomin. She has an extensive repertoire, ranging from Bach to contemporary music, and has performed several world premières. Many of her concerts have been recorded for television and radio.