  The neutron EDM experiment has played an important part over many decades in
shaping and constraining numerous models of CP violation. This review article
discusses some of the techniques used to calculate EDMs under various
theoretical scenarios, and highlights some of the implications of EDM limits
upon such models. A pedagogical introduction is given to the experimental
techniques employed in the recently completed ILL experiment, including a brief
discussion of the dominant systematic uncertainties. A new and much more
sensitive version of the experiment, which is currently under development, is
also outlined.
