According to the invasion criterion, stable coexistence requires that all species in a community increase in abundance when rare, which occurs when stabilizing mechanisms cause intraspecific competition to be stronger than interspecific competition. This simple principle has traditionally been applied to tests of local coexistence in a narrow range of ecological systems. However, new theory founded on the invasion criterion is emerging across ecological fields ranging from eco-evolutionary dynamics to global change to macroecology. Concurrently, straightforward methods for testing the invasion criterion have been proposed, but remain underused. Here, we identify the invasion criterion as a common thread linking emerging ecological theory, and we bring this theory together with the methods that can be used to test it. The invasion criterion has historically been applied to tests of local coexistence in a narrow range of ecological systems.New theory based on the invasion criterion is rapidly emerging, while new methods that allow researchers to test this principle across a broader range of systems have been introduced.We identify the invasion criterion as a common thread that links emerging theory across a range of ecological fields, and we bring this theory together with the methods that can be used to test it.We hope to facilitate the empirical application of the invasion criterion to a range of questions that reach beyond tests of local coexistence.