A review is given, in the modern context of applications, of the major important scientific results obtained by the scientists and graduates of St. Petersburg State University in the field of celestial mechanics and stellar dynamics. The second part of the review covers the following topics: estimates and calculation of the MOID parameter, problems of asteroid–comet hazard, dust complexes in the Solar System, rotational dynamics of planetary satellites, circumbinary dynamics, and methods for the discovery and determination of orbits of exoplanets.