Symmetry is everywhere - in natural objects, from crystals to living organisms, in manufactured articles of many kinds, and in art works from all cultures. Symmetry is a salient visual property that is detected efficiently and rapidly by the human visual system. In this paper, several decades of experimental research on human symmetry detection are reviewed. By examining the effects of several factors on symmetry detection, this research has revealed some important characteristics of how humans perceive symmetry. These characteristics constrain the general principles of putative underlying mechanisms and models of human symmetry detection. For example, the orientation of the axis of symmetry and its location in the visual field have effects that suggest that the bilateral symmetry of the visual system at cortical levels of the brain might partly determine the salience of vertical mirror symmetry. At the same time, there is a surprisingly high degree of flexibility and robustness that remains to be explained. Thus, symmetry provides a major challenge to model human flexibility and efficiency within the constraints of the biology of the visual system.