An overview is provided of the importance of molecular species containing unpaired electrons in catalytic systems, as revealed using ESR spectroscopy. The review aims to demonstrate the considerable extent of scientific progress that has been made in this broad topic during the past few decades. Studies of catalytically active surfaces, including zeolites, are surveyed, and the detection of radical species, formed as intermediates in their reactions, using matrix isolation and spintrapping techniques. Radical cation formation in zeolites is discussed, and the employment of muon spin rotation and relaxation techniques to study the mobility of labelled radicals in various porous and catalytic media. Among the specific types of catalytic media considered are those for photocatalysis, water splitting, degradation of environmental pollutants, hydrocarbon conversions, fuel cells and sensor devices employing graphene. The review concludes with recent developments in the study of enzymes and their reactions, using ESR-based methods.