Semiconductor nanoparticles afford an attractive workable method to degrade, indeed mineralize a vast number and variety of organic pollutants, and to dispose of trace quantities of toxic and/or precious metal ions or complexes found in wastewaters. The novel technology that has developed in the last two decades, but most actively in the last decade, implicates illumination of a semiconductor nanoparticulate photocatalyst (most often titania, TiO2, an n-type semiconductor); this has been referred to as Heterogeneous Photocatalysis, and comprises one of the Advanced Oxidation Technologies that also include W-H2O2 and UV-O-3 designed for environmental remediation by oxidative mineralization of organics in drinking waters and wastewaters. This chapter focusses on some of the fundamentals of this novel technology and will illustrate, using TiO2 as the photocatalyst of choice, some of the current understanding of processes that originate from absorption of photons by the photocatalyst and end up with the complete mineralization of organic pollutants to carbon dioxide.