This dissertation details two projects related to the genetic processes of recent evolution in human populations. Tying these two projects together is a reliance on haplotype-based methods, which leverage patterns of linkage across genetic variants, to better understand the evolutionary forces at play across the genome. The first chapter addresses the question, how often are signatures of recent positive selection shared across populations, vs. unique to a single population? After performing an initial scan for signatures of positive selection in 20 human populations, I used haplotype clustering to identify regions of the genome where the same sweeping haplotype is present in multiple populations. These signatures tend to be shared within continental groups; but I describe examples of sharing both within and across continents, and potential biological mechanisms under selection. In the second chapter, I develop methods to identify recurrent mutations, i.e. mutations that have occurred multiple times in a population, in large-scale population sequencing data. The first method relies on a likelihood ratio calculated from the probability distributions of the time to the most recent ancestor for recurrent and identical-by-descent variants. The second approach uses a Bayesian hierarchical model to assign variants to mixture proportions of identical-by-descent or recurrent variants. By identifying recurrent mutations, we can better understand the spectrum of recent mutations in human populations, the source of genetic variation driving evolution and a key factor in understanding recent demographic history.