This paper reviews empirical evidence for the detection of visual symmetries and explanatory theories and models of symmetry detection. First, mirror symmetry is compared to other types of symmetry. The idea that symmetry detection is preattentive is then discussed and other roles that attention might play in symmetry detection are considered. The major part of the article consists of a critical examination of the extensive literature about the effects on symmetry detection of several major factors such as the orientation of the symmetry axis, the location of the stimulus in the visual field, grouping, and perturbations. Constraints on plausible models of symmetry detection are derived from this rich database and several proposals are evaluated against it. As a result of bringing this research together, open questions and remaining gaps to be filled by future research are identified.