The purpose of the work presented in this thesis has been to investigate thermal transport in pure polystyrene as well as in a mixture of polystyrene and carbon dioxide. Another part of the work has been to calculate the anisotropy of the thermal conductivity in stretched polystyrene. To finally tie everything together, the most important part has been to understand thermal transport mechanisms on the basis of the thermal conductivity of polystyrene and thermal conductivity of several molecular liquids, amorphous polyamide-6,6 and crystalline polystyrene. In chapter 1 the nonequilibrium molecular dynamic methods for calculation of the thermal conductivity have been discussed. The methods have been well-known and described in literature in much detail. Additionally, recent improvements in the calculation of the thermal conductivity of molecular liquids, polymers and carbon nanotubes have been discussed. An analysis has been made of the influence of simulation parameters such as the use of thermostats, perturbation periods, the size of the system, and force field parameters on the calculated thermal conductivity. The ability of molecular dynamics simulations to predict thermodynamic properties is highly determined by the potential used to represent inter- and intramolecular interactions. As it has been discussed in chapter 1, the choice of the force field is of the great importance and has the greatest influence on the thermal conductivity calculated. In chapter 2 the thermal conductivity of atactic polystyrene (PS) swollen in supercritical CO2 as evaluated by reverse nonequilibrium molecular dynamics simulations (RNEMD) has been discussed. As experimental thermal conductivity values for the binary systems have not been reported, the computer simulations have been extended to the components PS and CO2, for which measured data is available. The comparison of calculated and experimental thermal conductivities of the components is a prerequisite for quantifying the capability of the present theoretical tools. The analysis offers a second benefit, i.e. the presentation of an analytical interpolation formula to relate the thermal conductivity of the components PS and CO2 to the thermal conductivity of the binary mixture. The thermal conductivity of PS-CO2 mixtures as a function of temperature, pressure and CO2 concentration by RNEMD simulations has been analyzed. Many polymers are highly anisotropic, for example crystalline polymers. Thermal conductivity is one of the quantities for which anisotropic behavior has been observed. The anisotropy of the thermal conductivity has been analyzed in several experimental and theoretical studies on polymers, such as amorphous polyamide-6,6 and polyethylene.2,4,8 In chapter 3 the anisotropy of the thermal conductivity of stretched atactic polystyrene swollen in supercritical CO2 by reverse nonequilibrium molecular dynamics simulations has been discussed. In chapter 4 all important steps and achievements that have been done during this work have been summarized and an outlook on the work that can be done in the future has been given. In the end of the dissertation one can find a list of the papers that have been published during this PhD work.