To predict and explain the behavior of others, one must understand that their actions are determined not by reality but by their beliefs about reality. Classically, children come to understand beliefs, including false beliefs, at about 4-5 y of age, but recent studies using different response measures suggest that even infants (and apes!) have some skills as well. Resolving this discrepancy is not possible with current theories based on individual cognition. Instead, what is needed is an account recognizing that the key processes in constructing an understanding of belief are social and mental coordination with other persons and their (sometimes conflicting) perspectives. Engaging in such social and mental coordination involves species-unique skills and motivations of shared intentionality, especially as they are manifest in joint attention and linguistic communication, as well as sophisticated skills of executive function to coordinate the different perspectives involved. This shared intentionality account accords well with documented differences in the cognitive capacities of great apes and human children, and it explains why infants and apes pass some versions of false-belief tasks whereas only older children pass others.