1. Are local ecological communities ever saturated with species? That is, do they ever reach a point where species from the regional pool are unable to invade the local habitat because of exclusion by resident species? 2. We review the theoretical evidence for saturation in various community models and find that non-interactive models predict the absence of saturation as expected, but that interactive models do not uniformly predict saturation. 3. Instead, models where coexistence is based on niche space heterogeneity predict saturation, whereas those where coexistence is based upon spatial heterogeneity yield mixed predictions. 4. Thus, theory says that species interactions are a necessary but not sufficient condition for local saturation in ecological time. 5. We then argue that unsaturated (Type I) assemblages are likely to be ubiquitous in nature and that even saturated (Type II) assemblages may not show hard limits to richness over evolutionary time-scales. 6. If local richness is not often saturated, then regional richness is freed from local constraint, and other limits on regional richness (which, in turn, limit local richness) become important, including phylogenetic diversification over evolutionary time-scales. 7. Our speculations inevitably suggest that the principal direction of control for species richness is from regional to local. If correct, then the key to community structure may lie in extrinsic biogeography rather than in intrinsic local processes, making community ecology a more historical science.