Most of our social interactions rest upon our ability to understand the behavior of others. But what is really at the basis of this ability? The standard view is that we understand the behavior of others because we are able to read their mind, to represent them as individuals endowed with mental states such as beliefs, desires and intentions. Without this mindreading ability the behavior of others would be meaningless for us. Over the last few years, however, this view has been undermined by several neurophysiological findings and in particular by the discovery of mirror neurons. The functional properties of these neurons indicate that motor and intentional components of action are tightly intertwined, suggesting that the basic aspects of intentional understanding can be fully appreciated only on the basis of a motor approach to intentionality. This paper has a dual objective: to develop this approach in order to account for the crucial role of motor intentionality in action and intention understanding below and before any meta-representational ability, and to shed new light on the ontogeny of mindreading, by explaining how the first forms of understanding in infants may be intentional in nature, even without presupposing any explicit and deliberate mentalizing.