Surfaces that exhibit reversible wettability toward water are extremely important for a variety of technological applications. In this context, the development of superhydrophobic and superhydrophilic surfaces for self-cleaning applications has been receiving a great deal of attention in the last few years. In this review, an overview of the current state-of-science and technology of self-cleaning surfaces is presented. The current understanding of physics of wetting leading to surfaces with predictive, controllable and reversible wettability is first presented. The review then focuses on materials, mainly metal oxides and their composites, employed for self-cleaning applications. It is shown that, although conventionally oxides and polymers are considered for self-cleaning applications, recent developments point toward the use of artificially engineered surfaces with hierarchical roughness. Applications of self-cleaning films in non-conventional areas such as protection of fabrics, solar cells and structures related to cultural heritage are discussed. The review ends with an outlook for the future in terms of science and technology of self-cleaning surfaces.