FIDE have just taken the decision to exclude teams from Russia and Belarus in any official FIDE team competition, at least for the foreseeable future. The most obvious effect of this decision is that both countries will not be able to take part in the upcoming chess Olympiad. This decision does not effect individual players, although in that case, the players themselves are required to play under the FIDE flag (or change federations).
In terms of how this effects the Olympiad itself, the loss of the Russian team does make it a little easier for other countries. However it is worth noting that Russia last won the Olympiad in 2002, while countries like Armenia, China and Ukraine have won it multiple times since. Of course the previous incarnation of the Russian team, the USSR, was absolutely dominant, winning every Olympiad from 1952 to 1974, and then again from 1980-1990. In that era they were able to draw on players from other republics, including Ukraine.
One of the players from the early years of the Soviet Olympiad team was David Bronstein, considered one of the most original thinkers in the game, and one of Ukraine's greatest players. Here is a game from his first Olympiad, against Henry Grob, who missed the chance to play his own opening (1.g4).
Grob,Henry - Bronstein,David I [B23]
Helsinki ol (Men) prel-C Helsinki (2), 1952
1. e4 c5 2. Nc3 g6 3. d4 cxd4 4. Qxd4 Nf6 5. e5 Nc6 6. Qf4 Nh5 7. Qe4 d6 8. exd6 Qxd6 9. Be3 Bg7 10. Nb5 Qb8 11. c3 O-O 12. Be2 a6 13. Nd4 Nxd4 14. Bxd4 Bf5 15. Qe3 Nf4 16. Kf1 e5 17. Bc5 Rd8 18. g4 Be6 19. h4 Qc8 20. f3 Qc6 21. Rh2 Rac8 22. Ba3 b5 23. Kf2 Nd5 24. Qe4 f5 25. Qb1 a5 26. c4 bxc4 27. h5 Nf4 28. Qc2 e4 29. hxg6 hxg6 30. Rd1 Rxd1 31. Bxd1 Nd3+ 32. Kf1 fxg4 33. fxg4 Rc7 34. Qa4 Rf7+ 35. Ke2 Bxg4+ 36. Kd2 c3+ 37. Ke3 Qb6+ 38. Kxe4 Qe6+ 0-1