A predictive understanding of the ecological impacts of nonnative species has been slow to develop, owing largely to an apparent dearth of clearly defined hypotheses and the lack of a broad theoretical framework. The context dependency of impact has fueled the perception that meaningful generalizations are nonexistent. Here, we identified and reviewed 19 testable hypotheses that explain temporal and spatial variation in impact. Despite poor validation of most hypotheses to date, evidence suggests that each can explain at least some impacts in some situations. Several hypotheses are broad in scope (applying to plants and animals in virtually all contexts) and some of them, intriguingly, link processes of colonization and impact. Collectively, these hypotheses highlight the importance of the functional ecology of the nonnative species and the structure, diversity, and evolutionary experience of the recipient community as general determinants of impact; thus, they could provide the foundation for a theoretical framework for understanding and predicting impact. Further substantive progress toward this goal requires explicit consideration of within-taxon and across-taxa variation in the per capita effect of invaders, and analyses of complex interactions between invaders and their biotic and abiotic environments.