GIVE[T]›to give something to someone and receive something similar from them: It's traditional for the two teams to exchange shirts after the game.
SHOP[T]›to take something back to the shop where you bought it and change it for something else: Could I exchange this shirt for a larger size?
exchange looks/smiles/words, etc›If two people exchange looks, smiles, words, etc, they look at each other/smile at each other/talk to each other, etc.: The couple opposite us sat through the whole meal without exchanging a word.