It is remarkable how well the human visual system can cope with changing viewpoints when it comes to recognising shapes. The state of the art in machine vision is still quite remote from solving such tasks. Nevertheless, a surge in invariance-based research has led to the development of methods for solving recognition problems still considered hard until recently. A nonmathematical account explains the basic philosophy and trade-offs underlying this strand of research. The principles are explained for the relatively simple case of planar-object recognition under arbitrary viewpoints. Well-known Euclidean concepts form the basis of invariance in this case. Introducing constraints in addition to that of planarity may further simplify the invariants. On the other hand, there are problems for which no invariants exist.