A general introduction, on an intuitive level, is presented to discrete symmetries of physical laws: P, C, T and CPT. The accurate measurement of the weak nuclear charge in atomic cesium serves as a precision test of the Standard Model. The discovery of the nuclear anapole moment, a new P odd electromagnetic multipole, in the cesium experiment gives a first-rate information on parity-nonconserving nuclear forces. New prospects in the field are discussed. Upper limits on the dipole moments 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.