The paper reviews solid-catalyzed oxidation and reduction processes for the treatment of wastewater that contains small concentrations of toxic compounds and for which separation is not economical while biological treatment is not feasible. Specifically, the objectives are (1) to understand the interactions between catalytic materials and various pollutants, (2) to provide a database for catalyst selection, and (3) to assess the potential of these processes for commercialization. The review suggests the following well-investigated solutions: (1) Supported metal (Ru/CeO2, Pt/CeO2, and Ru/C) and metal oxides (CuO-ZnO-CoO, MnO2/CeO2, CoO/Bi2O3, and V2O5/Al2O3) are the most promising catalysts for the destruction of refractory organic compounds with nearly 100% selectivity to CO2; (2) CoO/CeO2 and MnO2/CeO2 are the most active catalysts for ammonia oxidation at temperatures of 263-400°C; (3) activated carbon, preferably in the presence of copper ions, is an active catalyst for the oxidation of cyanides and sulfur-containing compounds; (4) catalytic hydrodechlorination (HDC) of chloroorganics and hydrodenitrification (HDN) of nitrates emerge as promising processes for wastewater treatment. To overcome mass-transfer resistance, catalysts should be constructed as fibers, cloth, or powder. Novel processes that incorporate separation at room temperature (e.g., by adsorption) and reaction at elevated temperatures are described. Suggestions for new directions of research are made.