P and T odd nuclear moments

We discuss the nuclear anapole moment, a new P odd, T even electromagnetic multipole. Its discovery in the cesium experiment gives a first-rate information on parity-nonconserving nuclear forces. New prospects in the field are considered. Upper limits on the electric dipole moments, which are P odd, T odd multipoles, of elementary particles and atoms are presented, and their physical implications discussed. The atomic experiments are demonstrated to be as informative in this respect as the neutron ones. Tremendous progress in the field can be expected from experiments at ion storage rings and linear electrostatic traps.