Natural selection and mutation are fundamental forces in molecular evolution: a better understanding of these processes in human populations is of intrinsic as well as clinical interest. My talk will describe some of our recent work in this area. First, developing a summary statistic to detect long-term balancing selection with application in humans. Second, an investigation on the extent to which recent, ongoing selective sweeps in humans are shared across human populations. Finally, work exploring variability in mutation rates across human populations as a function of broader windows of sequence context.