The anomalous adsorbate dynamics at surfaces in porous media studied by nuclear magnetic resonance methods. The orientational structure factor and Lévy walks J. Chem. Phys. 109, 6929 (1998) Recent years have seen significant progress in the NMR study of porous media from natural and industrial sources and of cultural significance such as paintings. This paper provides a brief outline of the recent technical development of NMR in this area. These advances are relevant for broad NMR applications in material characterization.