Orthology is a powerful refinement of homology that allows us to describe more precisely the evolution of genomes and understand the function of the genes they contain. However, because orthology is not concerned with genomic position, it is limited in its ability to describe genes that are likely to have equivalent roles in different genomes. Because of this limitation, the concept of 'positional orthology' has emerged, which describes the relation between orthologous genes that retain their ancestral genomic positions. In this review, we formally define this concept, for which we introduce the shorter term 'toporthology', with respect to the evolutionary events experienced by a gene's ancestors. Through a discussion of recent studies on the role of genomic context in gene evolution, we show that the distinction between orthology and toporthology is biologically significant. We then review a number of orthology prediction methods that take genomic context into account and thus that may be used to infer the important relation of toporthology.