Classical ecological theory predicts that ecological communities should only contain as many species as there are resources. Many ecosystems, however, seem to contain many more species than classical theory allows. Understanding this paradox is central to community ecology and biogeography. Niche-based models consider that differences and trade-offs between species’ life history traits stabilise species interactions and so allow coexistence. In stark contrast, neutral models assume that individuals at the same trophic level interact identically with conspecifics and heterospecifics (i.e. all species are equivalent), and this equivalence allows coexistence. Despite it seeming unlikely that species are equivalent, neutral models do predict some of the macroscopic properties of ecological communities surprisingly well. Although there are many neutral models, the best-known neutral model in the context of community ecology is that described by Hubbell (2001) in the Unified Neutral Theory of Biodiversity. We review the development of neutral theory in ecology and biogeography, consider its predictions and how they can be evaluated, and look at how neutral theory may develop in the future. This article focuses on species-rich plant communities, as they are, for the most part, the test-bed for the recent development and application of neutral models, but we also consider the application of neutral approaches to other taxonomic groups and ecosystem types.