Many animals, and in particular great apes, show evidence of culture, in the sense of having multiple innovations in multiple domains whose frequencies are influenced by social learning. But only humans show strong evidence of complex, cumulative culture, which is the product of copying and the resulting effect of cumulative cultural evolution. The reasons for this increase in complexity have recently become the subject of extensive debate. Here, we examine these reasons, relying on both comparative and paleoarcheological data. The currently best-supported inference is that culture began to be truly cumulative (and so, outside the primate range) around 500,000 years ago. We suggest that the best explanation for its onset is the emergence of verbal teaching, which not only requires language and thus probably coevolved with the latter's evolution but also reflects the overall increase in proactive cooperation due to extensive allomaternal care. A subsequent steep increase in cumulative culture, roughly 75 ka, may reflect the rise of active novelty seeking (curiosity), which led to a dramatic range expansion and steep increase in the diversity and complexity of material culture. A final, and continuing, period of acceleration began with the Neolithic (agricultural) revolution.