As populations diverge, genetic differences accumulate across the genome. Spurred by rapid developments in sequencing technology, genome-wide population surveys of natural populations promise insights into the evolutionary processes and the genetic basis underlying speciation. Although genomic regions of elevated differentiation are the focus of searches for 'speciation genes', there is an increasing realization that such genomic signatures can also arise by alternative processes that are not related to population divergence, such as linked selection. In this Review, we explore methodological trends in speciation genomic studies, highlight the difficulty in separating processes related to speciation from those emerging from genome-wide properties that are not related to reproductive isolation, and provide a set of suggestions for future work in this area.