The structure and/or the state of dislocation core often play a significant role in the glide process of the dislocation and hence control the plasticity of the crystal. We show various examples in this paper. (1) The yield stress of single crystals controlled by the Peierls mechanism for screw dislocation does not obey the Schmid law. (2) A narrow dissociation of the core can produce a plateau in the τy-Trelation. (3) Duality of the core structure can produce «yield stress anomaly». (4) Multiphonon emission at the core of dislocation in semiconducting crystals by non-radiative recombination of electron-hole pairs enhances drastically the dislocation mobility.