To talk about Bohr's idea of complementarity is not an easy task. No idea put forward to solve the paradoxes of atomic physics is so difficult to grasp, and at the same time so far reaching, as Bohr's notion of complementarity. It seems fair to say that few physicists ever fully understood the idea, and this is particularly true of the physicists of the present generation. On the other hand, Bohr held complementarity to be a very general approach for the description of Nature, not at all restricted to physics alone. In the following, I intend to describe in a non-technical way how the idea of complementarity arose in physics, and what it means. I must therefore leave out all details and subtleties, and my account will be of necessity rather schematic.