Over the past few decades, researchers have established artificial enzymes as highly stable and low-cost alternatives to natural enzymes in a wide range of applications. A variety of materials including cyclodextrins, metal complexes, porphyrins, polymers, dendrimers and biomolecules have been extensively explored to mimic the structures and functions of naturally occurring enzymes. Recently, some nanomaterials have been found to exhibit unexpected enzyme-like activities, and great advances have been made in this area due to the tremendous progress in nano-research and the unique characteristics of nanomaterials. To highlight the progress in the field of nanomaterial-based artificial enzymes (nanozymes), this review discusses various nanomaterials that have been explored to mimic different kinds of enzymes. We cover their kinetics, mechanisms and applications in numerous fields, from biosensing and immunoassays, to stem cell growth and pollutant removal. We also summarize several approaches to tune the activities of nanozymes. Finally, we make comparisons between nanozymes and other catalytic materials (other artificial enzymes, natural enzymes, organic catalysts and nanomaterial-based catalysts) and address the current challenges and future directions (302 references).