She graduated in 2003 from the Russian State Academy of Physical Education in Moscow as a certified professional chess trainer.

[13] In August 2006, she became the first Chess960 women's world champion after beating Germany's top female player Elisabeth Pähtz by 5½–2½.

[14] However, Kosteniuk's greatest success so far has been to win the Women's World Chess Championship 2008, beating in the final the young Chinese prodigy Hou Yifan with a score of 2½–1½.

[17] In the Women's World Chess Championship 2010 Kosteniuk was eliminated in the third round by the eventual runner-up, Ruan Lufei, and thus lost her title.

[21] In late May, Alexandra faced Ukrainian-American International Master Anna Zatonskih in the quarterfinal match of the 2019 Women's Speed Chess Championship, an online blitz and bullet competition hosted by Chess.com.

[26] In December she also achieved 2nd place in the Belt and Road World Chess Woman Summit, behind Hou Yifan.

[27] In August 2020, Alexandra was part of the Russian team which shared the gold medal with India in the Online Chess Olympiad.

Seeded 14th in the tournament, she won all of her classical matches without ever needing to play a tiebreak, defeating Deysi Cori, Pia Cramling, Mariya Muzychuk, Valentina Gunina and Tan Zhongyi, before winning the tournament with a 1.5 - 0.5 score against top seed Aleksandra Goryachkina in the finals.

[30] Kosteniuk ended the year by winning the women's world rapid championship in Warsaw, with an undefeated and unequalled 9.0 out of 11 score.