Here we report the Simons Genome Diversity Project data set: high quality genomes from 300 individuals from 142 diverse populations. These genomes include at least 5.8 million base pairs that are not present in the human reference genome. Our analysis reveals key features of the landscape of human genome variation, including that the rate of accumulation of mutations has accelerated by about 5% in non-Africans compared to Africans since divergence. We show that the ancestors of some pairs of present-day human populations were substantially separated by 100,000 years ago, well before the archaeologically attested onset of behavioural modernity. We also demonstrate that indigenous Australians, New Guineans and Andamanese do not derive substantial ancestry from an early dispersal of modern humans; instead, their modern human ancestry is consistent with coming from the same source as that of other non-Africans.