The transport of chemical species though porous media is of interest to environmental scientists and engineers alike. Identical physical phenomenon is usually observed among the transport behaviour of chemical species though a membrane, a solid adsorbent or through a contaminated sub-surface soil. The factors that determines the fate of pollutants (particularly persistent chemicals) are influenced by diffusion, dispersion and sorption which are related to pore-size distribution of the host material. In this presentation, I will dwell upon some fundamental aspects of transport behaviour though the porous media derived from the basic principles as well as some empirical approaches. Due to significant pore size variation in natural materials, often multi-dispersed modelling approach has been proposed to accommodate transport in a combined small and large pore networks. To that end, I will also discuss a new variant of bi-disperse model and an interfacial resistance model that is developed for species transport in hierarchical materials usually found in nature and also produced synthetically.