Causal independence of the simultaneous positions and momenta of two distinguishable particles in nonrelativistic physics and causal independence of events in two relatively spacelike regions of space-time in relativity are analyzed and discussed. This review paper formulates causal independence in a general and operational way and summarizes the inferences drawn from it in non-relativistic quantum mechanics, classical relativistic point mechanics, quantum field theory, and classical field theory. Special attention is given to the open question of the relationship between local independence (...) and commutativity in quantum field theory. (shrink)