Surface hydrides are ubiquitous in catalysis. However, their structures and properties are not as well-understood as those of their molecular counterparts, which have been extensively studied for the past 70 years. Hydrides isolated on surfaces have been characterized as stable entities on oxide surfaces or in zeolites. They have also been proposed as reaction intermediates in numerous catalytic processes (hydrogenation, hydrogenolysis, etc.). They have also been prepared via surface organometallic chemistry. In this review, we describe their key structural features and spectroscopic signatures. We discuss their reactivity and stability and also point out unexplored areas.