We analyze, classify, and compare the relative roles of different mechanisms of dislocation dragging, including elastic and inelastic scattering of acoustic and optical phonons by a moving dislocation (phonon wind, Raman scattering, flutter effect) and phonon relaxation (thermoelastic losses, phonon viscosity, relaxation of ``slow'' phonons). The estimates are carried out with allowance for the finite dimensions of the dislocation core and corresponding deviations of its elastic field from the relations known from the continual dislocation theory. We consider a number of qualitative effects connected with the emission of phonons by a dislocation in the case of stationary motion over the Peierls relief. We discuss the possible mechanisms whereby impurities affect the dynamic dragging of the dislocations. A brief review is presented of the experimental methods of investigating the dynamic mobility of dislocations. The theoretical results are compared with the experimental data on the magnitude and temperature dependence of the dynamic dragging.