We discuss two methods using slow neutrons to search for interactions which violate both parity (P) and time reversal (T) symmetry. The first and most well-known example is the continuing effort to find an electric dipole moment for the neutron. Another possibility is to search for a parity-odd and time reversal-odd amplitude in polarized neutron optical transmission through polarized nuclei. Both of these observables are null tests for P and T violation. Both of these methods also have the potential to improve the sensitivity compared to current limits on P and T violating amplitudes in nucleon-nucleon interactions by about two orders of magnitude.