Genome sequencing studies of de novo mutations in humans have revealed surprising incongruities with our understanding of human germline mutation. In particular, the mutation rate observed in modern humans is substantially lower than that estimated from calibration against the fossil record, and the paternal age effect in mutations transmitted to offspring is much weaker than expected from our longstanding model of spermatogenesis. I consider possible explanations for these differences, including evolutionary changes in life history parameters such as generation time and the age of puberty, a possible contribution from undetected post-zygotic mutations early in embryo development, and variation in cellular mutation rates at different stages of the germline. I suggest a revised model of stem cell state transitions during spermatogenesis, in which ‘dark’ gonial stem cells play a more active role than hitherto envisaged, with a long cycle time undetected in experimental observations. More generally, I argue that the mutation rate and its evolution depend intimately on the structure of the germline in humans and other primates.