We describe elementary concepts, up-to-date developments, and perspectives of the emerging field of nanoparticle enzyme mimics (so-called "nanozymes") at the interface of chemistry, biology, materials, and nanotechnology. The design and synthesis of functional enzyme mimics is a long-standing goal of biomimetic chemistry. Metal complexes, polymers and engineered biomolecules capturing the structure of natural enzymes or their active centers have been made to achieve high rates and enhanced selectivities. Still, the design of new "artificial enzymes" that are not related to proteins but with capacity of production and stability at industrial level, remains a goal. Inorganic nanoparticles bear this potential. Although it seems counterintuitive to compare nanoparticles and natural enzymes because they appear very different they share many common features: nano-size, irregular shape, and rich surface chemistry. These features enable nanomaterials to mimic reactions of natural enzymes. Representative examples with biomedical and environmental applications are given.