The design and development of many separation and catalytic process technologies require a proper quantitative description of diffusion of mixtures of guest molecules within porous crystalline materials. This tutorial review presents a unified, phenomenological description of diffusion inside meso- and micro-porous structures. In meso-porous materials, with pore sizes 2 nm < d(p) < 50 nm, there is a central core region where the influence of interactions of the molecules with the pore wall is either small or negligible; meso-pore diffusion is governed by a combination of molecule-molecule and molecule-pore wall interactions. Within micro-pores, with d(p) < 2 nm, the guest molecules are always under the influence of the force field exerted with the wall and we have to reckon with the motion of adsorbed molecules, and there is no "bulk" fluid region. The characteristics and physical significance of the self-, Maxwell-Stefan, and Fick diffusivities are explained with the aid of data obtained either from experiments or molecular dynamics simulations, for a wide variety of structures with different pore sizes and topology. The influence of adsorption thermodynamics, molecular clustering, and segregation on both magnitudes and concentration dependences of the diffusivities is highlighted. In mixture diffusion, correlations in molecular hops have the effect of slowing-down the more mobile species. The need for proper modeling of correlation effects using the Maxwell-Stefan formulation is stressed with the aid of examples of membrane separations and catalytic reactors.