We discuss several examples of applications of soft matter and statist
ical physics to various problems related to porous and fractured media
. The structure of porous media often displays multiple scale features
which can be analysed by neutron diffraction or electron microscopy a
nd can be approached by fractal models. Such characteristics are also
observed on the surface of natural fractures.The relation between vari
ous transport parameters such as permeability or conductivity introduc
e characteristic microscopic length scales which can sometimes be inde
pendently determined. In some cases, if the porous medium get clogged
or if the number of flow channels or fractures is low enough so that t
hreshold effects appear which can be analysed in terms of percolation
models. Disorder physics approaches are particularly useful to analyse
non miscible diphasic flows in some cases in which multiscale heterog
eneities of the fluid mixture composition appear. This is for instance
the case for very slow non wetting invasions and of the fast injectio
n of a low viscosity fluid : these processes can be described respecti
vely by the ''invasion percolation'' and the ''diffusion limited aggre
gation'' models. Finally tracer dispersion provides an application of
random walk models to disordered systems : examples of the response of
this measurement in partly saturated and double porosity media are pr
esented.