Ecological communities are diverse and species in them interact with each other in direct and indirect ways. However, this web of interactions is often neglected in studies trying to understand why some ecological communities are more susceptible to invasion by exotic species. Understanding the net effect of this plethora of interactions is important to make accurate predictions of the outcome of species invasions, and therefore to prioritize the management of exotic species once introduced in new ecosystems. This perspective aims to show that this limitation can be overcome by employing a set of tools recently developed within the field of coexistence theory. Specifically, these tools developed within a structural stability approach help us to understand how multispecies interactions both within and between trophic levels promote or limit the maintenance of species diversity. The advantage of this framework is that it can be applied to both competitive and trophic networks. The fundamental message here is that species interactions define a likelihood region for coexistence, and species can coexist when their demographic differences fall within this space. This framework allows us to include the effect of environmental variation, and it also works equally well when a native community faces the invasion of an exotic species or when a resident community already invaded faces invasions by new exotic species. Therefore, this framework presents a straightforward transition from the dichotomy of the invasive species-native community problem to more realistic scenarios such as novel ecosystems; ecosystems that contain exotic species and face new introductions sometimes under abrupt environmental changes. Overall, this perspective shows how to incorporate conceptually and methodologically a structural stability approach into the study of biological invasions.