Key words Dusty (complex) plasmas, dusty plasmas structures, magnetic field, ion drag force, plasmas magnetization. PACS 52.27.LwResults are described of experiments in studying the effect of magnetic field on dusty plasma structures in dc discharges. The levitation of dust particles in vertically oriented dc discharges is possible either in the vicinity of the flat surface of cathode (or of special additional electrode) or in an electrostatic trap which forms at the striation head during the stratification of positive column. The most interesting one of the observed effects is that of rotation of dust structures in the case of imposition of axial magnetic field. The rotation occurs about the discharge axis of symmetry with a velocity which is a nonmonotonic function of magnetic force. An increase in the field may cause the variation of direction of rotation for the opposite. An interpretation is given of the mechanism of rotation and of the inversion of its velocity. The rotation of dust structures is caused by the tangential component of ion drag force. It is demonstrated that the inversion is, in the final analysis, associated with the competition between two mechanisms of plasma recombination, namely, those on the discharge tube wall and on the surface of dust particles. When the magnetic field increases, the latter mechanism becomes predominating as a result of magnetization of plasma, and the inversion of rotation occurs.