Plasmas, being complex systems of a large number of non-linear processes, do not usually allow simple or even analytical solutions. Their evolution over time is described by different sets of equations depending on the parameters of the given plasma at hand. The main goal of this field, as in any other theoretical field of physics, is to bridge these various descriptions so that a complete understanding of these complex non-linear processes can be obtained. In this dissertation, plasma transport is studied with a model consisting of the 13-moments of the Fokker-Planck equation. In the highly collisional regime this model is compared against Chapman-Enskog expansions, such as Braginskii's transport equations. In the non-collisional regime this model is regularized and is then tested against analytical solutions to the kinetic Boltzmann equation. These validation tests show that a 13-moment plasma model can both reasonably approximate Braginskii's near equilibrium transport as well as offer a natural extension to non-equilibrium systems. Using the Extended Magnetohydrodynamic code PERSEUS, the 13-moment model thus provides a unique tool to study plasmas over a wide parameter regime.