Symmetry has a central role in the study of vision. The concept of symmetry has an ancient origin in considerations of visual appearance; in modern times, abstracted and formalized into Group Theory, it has found spectacular applications, far beyond the visible; but its importance for vision persists in many ways including: • As a non-accidental feature of an image that cues affordances, 3D structure or the semantic categories of object present. • As a redundant aspect of an image which many be exploited for simplicity and compactness of encoding. • As a salient feature that draws attention, and evokes distinctive brain responses. • As a constraint on priors on the distribution of structures to be found in the natural world. • As an aesthetic principle. • As a design principle for vision systems. • The original idea for a Special Issue came from a symposium at the European Conference in Visual Perception, in 2015, on the topic of brain responses to visual symmetry, but we have now extended the scope. This Special Issue is devoted to provide a shared place for cutting edge studies on how and why symmetry is processed and exploited by biological and artificial visual systems.