Sympatric speciation has always fascinated evolutionary biologists, and for good reason; it pits diversifying selection directly against the tendency of sexual reproduction to homogenize populations. However, different investigators have used different definitions of sympatric speciation and different criteria for diagnosing cases of sympatric speciation. Here, we explore some of the definitions that have been used in empirical and theoretical studies. Definitions based on biogeography do not always produce the same conclusions as definitions based on population genetics. The most precise definitions make sympatric speciation an infinitesimal end point of a continuum. Because it is virtually impossible to demonstrate the occurrence of such a theoretical extreme, we argue that testing whether a case fits a particular definition is less informative than evaluating the biological processes affecting divergence. We do not deny the importance of geographical context for understanding divergence. Rather, we believe this context can be better understood by modelling and measuring quantities, such as gene flow and selection, rather than assigning cases to discrete categories like sympatric and allopatric speciation.