The photocatalytic processes are normally implemented in an oxygen mediated aqueous environment. Therefore, the TiO2-water and TiO2-oxygen systems are of principal and practical interest in this field. It is not yet experimentally clear whether water adsorption on TiO2 surface is molecular or dissociative in nature, and this contradiction is due to different sample preparation methods, which lead to different surface morphologies. Furthermore, various atomic and molecular oxygen radical species exist in TiO2 mediated photocatalytic processes. Therefore, some difficulties emerge when the theoretical findings are compared with experimental data. Anatase TiO2 exposes mainly 001], 100] and 010] surfaces. Accordingly, the titanium atoms of five-fold coordinated on anatase TiO2 100] surface and the four-fold coordinated titanium atoms which exist at the defect sites, 100]- 010] boundaries, are modeled and considered for water and oxygen species adsorption, respectively. This book therefore, provides detailed mechanistic approaches, via a computational methodology, in order to advance the understanding of the adsorption of these essential small aquatic species and their stability.