An effective method to test time reversal invariance in the non-strange sector is to measure parity and time reversal violating (T,P-odd) electromagnetic moments, such as the static electric dipole moment. Parity and time reversal violating components in the nuclear force may produce P,T-odd moments in nuclei which, in turn, induce such moments in atoms. After a short introduction, we discuss the possibility that in some reflection-asymmetric heavy radioactive nuclei these moments are enhanced by several orders of magnitude. This opens the opportunity to improve significantly the limits on time reversal invariance. Some present and future experiments, which will test this idea, are mentioned. Recent theoretical results are briefly discussed.