Natural selection shapes patterns of genetic variation among individuals, populations, and species, and it does so differentially across genomes. The field of population genomics provides a comprehensive genome-scale view of the action of selection, even beyond traditional model organisms. However, even with nearly complete genomic sequence information, our ability to detect the signature of selection on specific genomic regions depends on choosing experimental and analytical tools appropriate to the biological situation. For example, processes that occur at different timescales, such as sorting of standing genetic variation, mutation-selection balance, or fixed interspecific divergence, have different consequences for genomic patterns of variation. Inappropriate experimental or analytical approaches may fail to detect even strong selection or falsely identify a signature of selection. Here we outline the conceptual framework of population genomics, relate genomic patterns of variation to evolutionary processes, and identify major biological factors to be considered in studies of selection. As data-gathering technology continues to advance, our ability to understand selection in natural populations will be limited more by conceptual and analytical weaknesses than by the amount of molecular data. Our aim is to bring critical biological considerations to the fore in population genomics research and to spur the development and application of analytical tools appropriate to diverse biological systems.