Effects of weak interactions: parity nonconservation and time-invariance violation, can be enhanced up to 106 times in compound nuclei. This factor is produced by (i) “simple” kinematical enhancement (ratio of the s-wave to the p-wave neutron capture amplitudes), and (ii) very large density of compound resonances (dynamical enhancement). The latter phenomenon should be generic to many complex many-body systems (rare-earth atoms, atomic clusters, quantum dots in solids, etc.), and is strongly related to the problem of quantum chaos. This review is devoted to the theoretical aspects of the problem. Statistical theory is used to calculate the r.m.s. value and the distribution of matrix elements of the weak perturbations between compound states. The behaviour of effects upon averaging over many compound resonances is studied. It is shown that the effects, though of random sign, are not suppressed by such averaging. Valence mechanism, rotational doublet states, doorway states are considered as possible sources of regular contributions to the effect. The renormalization of weak interaction by the strong interaction and its relation to the problem of π-mesons in nuclear matter is discussed.