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In this thesis we studied several aspects of polymer dynamics simulations. The first part of the thesis deals with the crystallization in polymeric materials; there, it is shown that a single molecule in solution is able to reach its equilibrium configuration, which represents the minimum of the free energy landscape. For the first time, an analytical model is proposed to take into account the effects related to the short length of the loop at the crystal boundaries. The second part of the thesis is devoted to develop faster stochastic algorithms for the integration of the equation of motion; our attention is addressed in particular toward symplectic integration schemes, which allow to achieve longer time steps. The last part of the thesis tackles the problem of glass transition, proposing a possible universal scaling which is able to link the fast, local motions of the polymer, with its slow, structural properties.