This review concerns basic research on cellulases and cellulose-specific carbohydrate-binding modules (CBMs). As a background, glycosyl hydrolases are also briefly reviewed. The nomenclature of cellulases and CBMs is discussed. The main cellulase-producing organisms and their cellulases are described. Synergy, enantioseparation, cellulases in plants, cellulosomes, cellulases and CBMs as analytical tools and cellulase-like enzymes are also briefly reviewed.