Disordered porous networks are important examples of confining geometries. A challenging problem is to couple the morphology and the topology of such disordered systems with the diffusion and the reactive properties of embedded fluids (gases or liquid) inside the porous medium. Looking at the properties of the self-diffusion propagator, we first discuss how the geometric confinement influences the molecular diffusion and how the coupling between interfacial geometry and transport evolves in space and time. In the long time regime, two specific situations are presented. First, we focus on transport properties inside a membrane-like disordered matrix, the sponge phase (symmetric or asymmetric). Second, we discuss some basic properties of the Knudsen diffusion. The particular coupling with the pore network geometry allows to analyse this transport process in term of the continuous time random walk formalism (C.T.R.W.). An interesting consequence for some specific disordered porous media or "low dimension" geometries is a transition from a Gaussian diffusion to a Levy walk. Finally, excitation and relaxation kinetics are discussed. More specifically, NMR relaxation of water inside a Vycor glass is investigated and a comparison with recent experimental results is presented.
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