 It has been an old idea by Bohr that central conceptual features of quantum theory, such as complementarity, are also of pivotal significance outside the domain of physics. In fact, Bohr became familiar with complementarity through the psychologist Edgar Rubin and, more indirectly, William James (Holton 1970) and immediately saw its potential for quantum physics. Although Bohr was also convinced of the extraphysical relevance of complementarity, he never elaborated this idea in concrete detail, and for a long time after him no one else did so either. This situation has changed: there are now a number of research programs generalizing key notions of quantum theory in a way that makes them applicable beyond physics.