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The dependence of dislocation mobility on temperature, stress, and alloy composition is a key to describing plastic deformation in metals. A special case is the plasticity of body-centered cubic (bcc) metals and alloys, where the motion of screw dislocations is the rate-limiting process. This paper presents a comprehensive study of the motion of edge and screw dislocations in pure bcc metals (W, Mo and Nb) and complex concentrated alloys. The study involved large-scale atomistic simulations, through which screw dislocation velocities were computed for both athermal and thermally activated regimes. The simulations revealed that the mobility of the screw dislocations shows a strong non-Arrhenius temperature behavior. This is particularly observed for bcc complex alloys. It is also shown that, with an accurate calculation of the dislocation mobility function, the measured plasticity properties can be predicted with sufficient accuracy over a wide temperature range.