Functional relationships involving species richness may be unimodal, monotonically increasing, monotonically decreasing, bimodal, multimodal, U-shaped, or with no discernable pattern. The unimodal relationships are the most interesting because they suggest dynamic, nonequilibrium community processes. For that reason, they are also contentious. In this paper, we provide a wide-ranging review of the literature on unimodal (humpbacked) species richness-relationships. Though not as widespread as previously thought, unimodal patterns of species richness are often associated with disturbance, predation and herbivory, productivity, spatial heterogeneity, environmental gradients, time, and latitude. These unimodal patterns are contingent on organism and environment; we examine unimodal species richness-curves involving plants, invertebrates, vertebrates, plankton, and microbes in marine, lacustrine, and terrestrial habitats. A goal of future research is to understand the contingent patterns and the complex, interacting processes that generate them.