Only among humans is teaching intentional, socially structured, and symbolically mediated. In this chapter, evidence regarding the evolution of the mindreading and communicative capacities underlying intentional teaching is reviewed. Play, rehearsal, and apprenticeship are discussed as central to the analyses of teaching. We present a series of levels of teaching. First of all, we separate non-intentional from intentional teaching. For non-intentional teaching, we discuss facilitation and approval/disapproval and analyze examples from non-human species. We then distinguish between six levels of intentional teaching: (1) intentional approval/disapproval, (2) drawing attention, (3) demonstrating, (4) communicating concepts, (5) explaining concept relations, and (6) narrating. We hypothesize that level after level has been added during the evolution of teaching. We analyze communicative requirements for the levels, concluding that displaced communication is required for level 4 and symbolic language only for levels 5 to 6. We focus on the role of demonstration and pantomime and argue that pantomime has been instrumental in the evolution of language. We present archaeological evidence for when the different levels of teaching emerge. We argue that learning Oldowan technology requires teaching by demonstration, and that learning Acheulean hand-axe technology requires communicating concepts. It follows that several levels of intentional teaching predate homo sapiens.