There are seemingly compelling reasons for expecting the laws of physics to be unchanged under various symmetry transformations. However, during the last fifteen years it has been discovered that many of these symmetries are in fact broken. The search for the electric dipole moment of the neutron has already made, and will continue to make, an important contribution to the understanding of this fascinating and fundamental problem. The experimental limits of sensitivity can be understood in terms of the Heisenberg uncertainty principle and the achievable limits for such things as the electric field strengths and observation times in various systems. The two experimental methods used to date are neutron beam magnetic resonance and crystal diffraction. New methods which have been proposed, such as that using bottled neutrons and further work on existing methods, promise a considerable improvement in sensitivity in the next few years.