In the world of membrane proteins, topology defines an important halfway house between the amino-acid sequence and the fully folded three-dimensional structure. Although the concept of membrane-protein topology dates back at least 30 years, recent advances in the field of translocon-mediated membrane-protein assembly, proteome-wide studies of membrane-protein topology and an exponentially growing number of high-resolution membrane-protein structures have given us a deeper understanding of how topology is determined and of how it evolves.