The activity in our laboratory and in collaboration with other laboratories in applying fractal geometry for the characterization of irregular surfaces and materials and for the analysis of molecular interactions with such objects are summarized in this report. Most of the studies were performed on the xerogel of silica. Various theories and experimental techniques have been employed for this purpose. They include adsorption studies, computerized image analyses in one (boundary lines), two (textures) and three (proteins) dimensions; non-radiative, Förster-type, one step electronic energy transfer (EET); small angle X-ray scattering; and analysis of chemical reactivity of fractal objects. The relation between porosity and fractal dimension has been studied by EET, by the photophysics of adsorbed pyrene and by monolayer adsorption studies. A direct method for the determination of adsorption conformations has been developed. Limitations of the fractal approach have been identified and outlined.