Event-by-event simulation of quantum phenomena

A discrete-event simulation approach is reviewed that does not require the knowledge of the solution of the wave equation of the whole system, yet reproduces the statistical distributions of wave theory by generating detection events one-by-one. The simulation approach is illustrated by applications to a two-beam interference experiment and two Bell test experiments, an Einstein-Podolsky-Rosen- Bohm experiment with single photons employing postselection for pair identification and a single-neutron Bell test interferometry experiment with nearly 100% detection efficiency.