Population geneticists have long sought to understand the contribution of natural selection to molecular evolution. A variety of approaches have been proposed that use population genetics theory to quantify the rate and strength of positive selection acting in a species' genome. In this review we discuss methods that use patterns of between-species nucleotide divergence and within-species diversity to estimate positive selection parameters from population genomic data. We also discuss recently proposed methods to detect positive selection from a population's haplotype structure. The application of these tests has resulted in the detection of pervasive adaptive molecular evolution in multiple species.