The invasion paradox describes the co-occurrence of independent lines of support for both a negative and a positive relationship between native biodiversity and the invasions of exotic species. The paradox leaves the implications of native-exotic species richness relationships open to debate: Are rich native communities more or less susceptible to invasion by exotic species? We reviewed the considerable observational, experimental, and theoretical evidence describing the paradox and sought generalizations concerning where and why the paradox occurs, its implications for community ecology and assembly processes, and its relevance for restoration, management, and policy associated with species invasions. The crux of the paradox concerns positive associations between native and exotic species richness at broad spatial scales, and negative associations at fine scales, especially in experiments in which diversity was directly manipulated. We identified eight processes that can generate either negative or positive native-exotic richness relationships, but none can generate both. As all eight processes have been shown to be important in some systems, a simple general theory of the paradox, and thus of the relationship between diversity and invasibility, is probably unrealistic. Nonetheless, we outline several key issues that help resolve the paradox, discuss the difficult juxtaposition of experimental and observational data (which often ask subtly different questions), and identify important themes for additional study. We conclude that natively rich ecosystems are likely to be hotspots for exotic species, but that reduction of local species richness can further accelerate the invasion of these and other vulnerable habitats.