This Chapter considers principles of the neutron-and x-ray scattering-based porosimetry, which exploits contrast variation and contrast matching method. The coherent scattering from porous solids arises largely from the contrast between the empty and filled pores. A porous medium is exposed to a solvent vapor having the same neutron scattering length density or electron density as the matrix skeleton. The smallest pores are filled with a condensed liquid already at low relative pressure, followed by filling of progressively larger pores. Thus, measured as a function of the relative pressure, SAS probes sub-populations of pores of increasing average size, which is calculated using the Kelvin equation. Illustrative examples are given of how SAS can be used for structural characterization of various types of porous materials including low-dielectric constant polymer films, porous silicas, carbonaceous materials, and Nafion membranes.