Abstract <p>This work provides an overview of the research of employees of the Department and Laboratory of Physical Mechanics of St. Petersburg University that are devoted to modeling the dynamics of natural and man-made microparticles in space plasma. Special attention is given to several major results: (i) the existence of three possible regimes of vertical oscillations of a dust particle over the Moon’s surface; (ii) the identification of possible mechanisms for the long-term retention of man-made microparticles in near-Earth space; (iii) the application of methods of Kolmogorov–Arnold–Moser (KAM) theory for the proof of conservation of orbital parameters for a microparticle with constant electric charge; (iv) determination of the conditions for applicability of the canonical formulation of the problem regarding the motion of a particle with locally equilibrium electric charge in near-Earth space; and (v) generalization of results of analytical modeling for a case of variable electric charge. Other results are given short enough.</p>