This article is based on the idea that paintings carry much of their cultural power by being ways of embodying states of mind in physical material. It follows that the understanding we have of how people infer mental states in others can also be used to address how we respond to visual art: our facility for inferring mental states can help us understand paintings. In pursuing this argument, I discuss first how artists make meaning in paintings by a process that embodies mental states within a formal structure. Second, I support the notion of a link between the formal structure of art and mental states with evidence from my studies of children's drawings. Third, by analogy with the way we relate to another person's mental states, I look in more detail at the process by which we 'read' a painting and in consequence develop an aesthetic relationship to it.