One of the central goals of evolutionary biology is to understand the genetic basis of adaptive evolution. The availability of nearly complete genome sequences from a variety of organisms has facilitated the collection of data on naturally occurring genetic variation on the scale of hundreds of loci to whole genomes. Such data have changed the focus of molecular population genetics from making inferences about adaptive evolution at single loci to identifying which loci, out of hundreds to thousands, have been recent targets of natural selection. A major challenge in this effort is distinguishing the effects of selection from those of the demographic history of populations. Here we review some current progress and remaining challenges in the field.