The degree to which adaptation in recent human evolution shapes genetic variation remains controversial. This is in part due to the limited evidence in humans for classic “hard selective sweeps,” wherein a novel beneficial mutation rapidly sweeps through a population to fixation. However, positive selection may often proceed via “soft sweeps” acting on mutations already present within a population. Here we examine recent positive selection across six human populations using a powerful machine learning approach that is sensitive to both hard and soft sweeps. We found evidence that soft sweeps are widespread and account for the vast majority of recent human adaptation. Surprisingly, our results also suggest that linked positive selection affects patterns of variation across much of the genome, and may increase the frequencies of deleterious mutations. Our results also reveal insights into the role of sexual selection, cancer risk, and central nervous system development in recent human evolution.