Twinned crystals are the subject of intensive investigation since the dawn of crystallography, because of their peculiar, eye-catching morphology. The occurrence of twins affects the physical properties of materials and can be a serious hindrance to the solution and refinement of the crystal structure. In this review we present basic definitions and terminology, a brief survey of the formation mechanism of twins, the reticular and structural approach to explain their occurrence and a few examples. The presence of a substructure shared by the twinned crystals is considered the key feature for the formation of twins. This common substructure can be found by determining first of all a common sublattice, and then by identifying those crystallographic orbits which possess, in their eigensymmetry, operations whose linear part coincide with the twin operation. The orientation and location of the composition surface plays, however, a fundamental role in determining the degree of structural restoration which defines the common substructure. Examples in staurolite, feldspars and an organic co-crystal composed of N-iodosaccharin and pyridine, all taken from the literature, are presented.