Each FIDE recognized chess association can enter a team into the Olympiad. Each team is made of up to five players, four regular players and one reserve (prior to the tournament in Dresden 2008 there were two reserves). Initially each team played all other teams but as the event grew over the years this became impossible. At first team seeding took place before the competition. Later certain drawbacks were recognized with seeding and in 1976 a Swiss tournament system was adopted.

The trophy for the winning team in the open section is the Hamilton-Russell Cup, which was offered by the English magnate Frederick Hamilton-Russell as a prize for the 1st Olympiad (London 1927). The cup is kept by the winning team until the next event, when it is consigned to the next winner. The trophy for the winning women's team is known as the Vera Menchik Cup in honor of the first Women's World Chess Champion.

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