Interest in fluids with strong magnetic properties has developed in recent years in connection with technical applications. Artificially created magnetic fluids are suspensions of very fine ($\sim10^{-6}$ cm) particles of ferromagnetic material in ordinary (as a rule nonconducting) liquids. This review briefly describes the methods of preparation and considers the stability problems of magnetic colloids. It deals principally with their physical and hydrodynamic properties. It summarizes the results of theoretical and experimental investigations of the effect of a magnetic field on the equilibrium conditions and on the character of the motion of the suspensions. A considerable part of the article is devoted to an analysis of critical phenomena--instability of the free surface of the liquid in an external field and thermoconvective instability. The mechanisms of relaxation of the magnetization of a suspension are discussed; the most important of these are rotational Brownian motion of the particles and the N\'eel fluctuation mechanism, which leads to the superparamagnetism of subdomain particles of a ferromagnetic material. Important differences are noted between the hydrodynamics of suspensions of superparamagnetic and of ferromagnetic particles. In the latter case it is necessary to take account of rotation of the particles themselves, which greatly complicates the picture of the interaction of hydrodynamic and magnetic phenomena. Consideration is given to various effects caused by internal rotation: anisotropy of the viscosity and of the magnetic susceptibility, entrainment of the suspension by a rotating field, and dependence of the kinetic coefficients on the field intensity.