  This review presents the state of the art on the theory, molecular
simulation, and coarse-grained strategies applied to the transport of gases and
liquids in nanoporous materials (pore size in the range 1 - 100 nm). Recent
advances in the understanding of molecular diffusion and transport under
thermodynamic gradients in nanoporous adsorbents are discussed with special
emphasis on small molecules in zeolites, active carbons, metal organic
frameworks, but also in nanoporous materials with larger pores such as ordered
and disordered mesoporous oxides. We provide a description of the fundamentals
and principles of the different atom-scale and mesoscopic methods as well as of
the theoretical formalisms that can be used to address such an important
problem. Special attention is paid to the investigation of different molecular
transport coefficients - including the so-called self, collective and transport
diffusivities - but also to the determination of free energy barriers and their
role in overall adsorption/separation process rates. We also introduce other
available approaches such as hierarchical simulations and upscaling strategies.
