A complete specification of the microstructure of a realistic porous medium is impractical. The present chapter discusses possibilities for characterizing porous media without specifying a porous geometry in all its detail. As emphasized in the introduction this is the main theoretical task. There are two general approaches: One approach constructs simplified geometric models for each specific porous medium of interest. The other approach attempts to find general characterizations for large classes of porous media which are less specific but more widely applicable. This latter approach will be discussed first.