[1] He beat some world champions: Vasily Smyslov at the Moscow Spartakiad 1974, Tal at Sochi 1970, and a young Garry Kasparov at the 1978 Soviet Championship.

Tseshkovsky himself almost qualified for the World Championship candidates matches when he finished fourth in the 1976 Manila Interzonal, one place lower than was needed to progress to the next stage.

In 2010, he also tied for 2nd-4th with Algimantas Butnorius and Nikolai Pushkov in the European Seniors’ Rapid Championship, which was won by Viktor Kupreichik.

Tseshkovsky maintained a high standard of chess throughout his career, registering his highest Elo rating of 2600 in October 2005.

As a coach, he assisted with the training of many high-profile players including Vladimir Kramnik, Bartlomiej Macieja and Boris Savchenko.