A brief review of the theoretical models which describe specific plastic deformation mechanisms in ultrafine-grained materials with nanotwinned structure (nanotwinned materials) is presented. In particular, micromechanism of nanotwin widening and micromechanism of combined action of lattice dislocation slip and twin boundary migration in nanotwinned materials are considered. Dependence of the flow stress on the plastic strain in nanotwinned cooper (Cu) is calculated. Also, dependence of the yield stress on twin thickness in nanotwinned cooper (Cu) is theoretically described. Our theoretical results and their comparison with corresponding experimental data in the exemplary case of nanotwinned copper (Cu) are discussed.