He has represented Ukraine in the 2005 World Team Chess Championship and in the Chess Olympiad in 2006 and 2008, winning team gold medals on both Olympiad occasions. In the Chess World Cup 2005, he made it to the third round before being knocked out. Areshchenko tied for first in the European Individual Chess Championship in 2012, and later that year, won the European Rapid Chess Championship.
In 2013, he won the 2nd Indonesia Open Chess Championship. He also competed in the Chess World Cup 2013, but was eliminated in the first round. Also in 2013, Areshchenko won the Al Ain Classic tournament.