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Recent transitions from coral to macroalgal dominance on some tropical reefs have engendered debate about their causes and effects. A widely accepted view is that reef environments support stable, alternative coral or non-coral assemblages, despite the lack of evidence to support this hypothesis. Confusion in the literature stems from (1) misunderstanding theory; and (2) conflating a switch between alternative stable states with a shift in the phase portrait of a single equilibrial system caused by a persistent change, or trend, in the environment. In the present paper we outline the conceptual derivation of the hypothesis of alternative stable states, distinguish it from the phase-shift hypothesis, and discuss the evidence required to support each one. For cases in which firm conclusions can be drawn, data from fossil and modern reefs overwhelmingly support the phase-shift hypothesis rather than the hypothesis of alternative stable states. On tropical reefs, a given environment evidently supports at most a single stable community. Corals dominate environments that are disturbed primarily by natural events and have small anthropogenic impacts. In such environments, macroalgae dominate a stage during some successional trajectories to the stable, coral-dominated community. In anthropogenically perturbed environments, the resilience of the coral-dominated community is lost, precipitating phase shifts to communities dominated by macroalgae or other noncoral taxa. The implication for reef management and restoration is both substantial and optimistic. To the extent that the environments of degraded reefs are restored, either passively or actively, the communities should return to coral dominance.