Social neuroscience provides insights into the neural correlates of the human capacity to explain and predict other people's intentions, a capacity that lies at the core of the Theory of Mind (ToM) mechanism. Results from neuroimaging research describe a widely distributed neural system underlying ToM, including the right and left temporo-parietal junctions (TPJ), the precuneus, and the medial prefrontal cortex (MPFC). Nevertheless, there is disagreement in the literature concerning the key region for the ToM network. Some authors point to the MPFC, others to the right TPJ. In the effort to make a contribution to the debate, we propose a model of a dynamic ToM network consisting of four regions. We also introduce a novel theoretical distinction among varieties of intention, which differ by the nature of an individual's pursued goal (private or social) and by the social interaction's temporal dimension (present or future). Our results confirm the crucial role of both the MPFC and the right TPJ, but show that these areas are differentially engaged depending on the nature of the intention involved. Whereas the right TPJ and the precuneus are necessary for processing all types of prior intentions, the left TPJ and the anterior paracingulate cortex are specifically involved in the understanding of social intention. More specifically, the left TPJ is activated only when a subset of social intentions are involved (communicative intentions). Taken together, these results demonstrate the progressive recruitment of the ToM network along the theoretical dimensions introduced in the present paper.