Event-by-event simulation of quantum phenomena

In this talk, I discuss recent progress in the development of simulation algorithms that do not rely on any concept of quantum theory but are nevertheless capable of reproducing the averages computed from quantum theory through an event-by-event simulation. The simulation approach is illustrated by applications to single-photon Mach-Zehnder interferometer experiments and Einstein-Podolsky-Rosen-Bohm experiments with photons.