Nanoporous materials are currently of great interest. Examples include membranes, catalyst, adsorbents, low-dielectric materials, skin and biological tissues. These materials, depending on their pore space morphology, contain a range of pore sizes. However, the main resistance to the transport process is offered by interconnected nano- and mesopores. Because of the exceedingly small sizes of the pores, the behavior of fluids and their mixtures inside such pores is very different from that in the bulk. Hence, one must resort to molecular dynamics simulations in order to gain a better understanding of transport of fluid mixtures in such materials. Since transport in such materials takes place under an external driving force, such as a chemical potential or pressure gradient, one must use non-equilibrium molecular dynamics simulations, which are far more complex than equilibrium MD methods, especially when one wishes to simulate transport of fluids in a three-dimensional pore structure. We describe recent advances in understanding transport of fluid mixtures in nanoporous materials using NEMD methods. We also describe a statistical mechanical theory that provides adequate description of some of the phenomena that occur in nanopores during transport of fluid mixtures.