This article reviews the research of Fedor Vasilievich Shugaev, Doctor of Physical and Mathematical Sciences and Professor at the Faculty of Physics of M. V. Lomonosov Moscow State University. Over a career at MSU spanning more than six decades, Professor Shugaev has published 146 journal articles, 4 monographs, 46 conference papers and 83 invited talks, and supervised twelve Candidate-of-Sciences dissertations and twenty diploma theses. The main research lines covered below are the propagation and reflection of shock waves; shock-wave interaction with vortices, acoustic disturbances and turbulent fluctuations; shock-wave dynamics in low-temperature and discharge plasmas; the geometry and stability of magnetised and astrophysical bow shocks; Navier–Stokes-based methods for vortex acoustics; laser-beam propagation through the turbulent atmosphere; and a recent cycle of work in theoretical astrophysics.