 One natural part of such a theory would be a purely structural necessary and sufficient condition for two structures to be elementarily equivalent. Roland Fraïssé, a French-Algerian, was the first to find a usable necessary and sufficient condition. It was rediscovered a few years later by the Kazakh logician A. D. Taimanov, and it was reformulated in terms of games by the Polish logician Andrzej Ehrenfeucht. The games are now known as Ehrenfeucht-Fraïssé games, or sometimes as back-and-forth games. They have turned out to be one of the most versatile ideas in twentieth-century logic. They adapt fruitfully to a wide range of logics and structures.