Quantum chaos and nuclear structure

The quantum level statistics were studied for the first time in nuclear spectra 60 years ago [I.I. Gurevich, JEPT 9 (1939) 1283]. Now, we know that atomic nuclei and complex atoms are good examples of mesoscopic quantum systems where the effects of quantum many-body chaos are clearly seen both in spectra and in the properties of complicated wave functions of stationary states. We present a short and subjective review of those ideas, applications to nuclear structure, and open problems.