In 1997 Morozevich was the top seed at the World Junior Chess Championship, but lost to the eventual champion, American Tal Shaked, in a bishop and knight checkmate.

In beginning of 2000 Morozevich participated at the Corus chess tournament in Wijk aan Zee and finished fifth out of 14 players.

In Wijk aan Zee 2001 Morozevich became the first player to defeat World Champion Vladimir Kramnik after beating him with black.

In the 2001 FIDE World Championship, Morozevich beat Nugzar Zeliakov, Krishnan Sasikiran and Mikhail Gurevich before losing in tie-breaks in the fourth round against the eventual winner of the event Ruslan Ponomariov.

In September 2005, Morozevich played in the FIDE World Chess Championship 2005 in San Luis, Argentina, taking fourth place behind Veselin Topalov, Anand and Peter Svidler.

[3] In June 2011 he won the Russian Championship Higher League in Taganrog with 8/11, earning a spot in the Superfinal, in which he came second behind the eventual winner Peter Svidler.

[4] In October Morozevich won the Saratov Governor's Cup in Russia with a score 8½/11, one and a half points ahead of the field, and a performance of 2917.

[5] In February 2012 Morozevich came first in the Vladimir Petrov Memorial, a rapidplay tournament with the time control of 15 minutes plus 6 seconds per move.

[7] Morozevich won the Magistral Ciutat de Barcelona tournament in 2015 on tiebreak over Axel Bachmann, having played more games with the black pieces.