The enzyme-mimicking nature of versatile nanomaterials proposes a new class of materials categorized as nano-enzymes, ornanozymes. They are artificial enzymes fabricated by functionalizing nanomaterials to generate active sites that can mimic enzyme-like functions. Materials extend from metals and oxides to inorganic nanoparticles possessing intrinsic enzyme-like properties. High cost, low stability, difficulty in separation, reusability, and storage issues of natural enzymes can be well addressed by nanozymes. Since 2007, more than 100 nanozymes have been reported that mimic enzymes like peroxidase, oxidase, catalase, protease, nuclease, hydrolase, superoxide dismutase, etc. In addition, several nanozymes can also exhibit multi-enzyme properties. Vast applications have been reported by exploiting the chemical, optical, and physiochemical properties offered by nanozymes. This review focuses on the reported nanozymes fabricated from a variety of materials along with their enzyme-mimicking activity involving tuning of materials such as metal nanoparticles (NPs), metal-oxide NPs, metal-organic framework (MOF), covalent organic framework (COF), and carbon-based NPs. Furthermore, diverse applications of nanozymes in biomedical research are discussed in detail.