The Aharonov-Bohm (A -B) and Aharonov-Casher (A - C) effects have, in recent years, been subjected to experimental verification using electron as well as neutron interferometry. This paper summarises these effects, concentrating on the neutron experiments, and discusses future possibilities. The refinments of the single crystal interferometer had allowed first-order sensitivity to the A - C phase shift to be achieved. Within experimental uncertainty, no measurable magnetic (or vector) A - B effect has been found for neutrons. A scalar A -B experiment with neutrons is now underway at the Missouri Research Reactor, as a collaboration between the University of Melbourne and the University of Missoury. It uses neutrons for exploring the phase shift caused by a scalar potential. A brief description of the actual experiment is given. 17 refs., 3 figs.