Single layer transition metal sulfides (SLTMS) such as MoS2, WS2, and ReS2, play an important role in catalytic processes such as the hydrofining of petroleum streams, and are involved in at least two of the slurry-catalyst hydroconversion processes that have been proposed for upgrading heavy petroleum feed and other sources of hydrocarbon fuels such as coal and shale oils. Additional promising catalytic applications of the SLTMS are on the horizon. The physical, chemical, and catalytic properties of these materials are reviewed in this report. Also discussed are areas for future research that promise to lead to advanced applications of the SLTMS.