What are the mechanisms enabling primates to display their complex social skills? And in particular, what makes humans different? A common view prefigures a sharp distinction between humans as mind readers and all nonhuman primates species, confined to behavior reading. This distinction is held to be the result of a discontinuity in the evolution of social cognition. We challenge this view by positing that behavior reading and mind reading may not constitute two autonomous, encapsulated realms. Apparently different cognitive strategies may be underpinned by similar functional mechanisms, which in the course of evolution acquire increasing complexity and are exapted to sustain more sophisticated new cognitive skills. We discuss the role of mirror neurons in monkeys and humans in relation to the ascription of intentions to others as a paradigmatic case in support of our thesis of a cognitive continuity within the evolution of primate social cognition.