Enzyme-mimicking nanomaterials (nanozymes) with antioxidant activity are at the forefront of research efforts towards biomedical and industrial applications. The selection of enzymatically active substances and their incorporation into novel inorganic nanozyme structures is critically important for this field of research. To this end, the fabrication of composites can be desirable as these can either exhibit multiple enzyme-like activities in a single material or show increased activity compared to the nanozyme components. Conversely, by modifying the structure of a nanomaterial, enzyme-like activities can be induced in formerly inert particles. We identify herein the three main routes of composite nanozyme synthesis, namely, surface functionalization of a particle with another compound, heteroaggregation of individual nanozymes, and modification of the bulk nanozyme structure to achieve optimal antioxidant activity. We discuss in particular the different inorganic support materials used in the synthesis of nanozyme architectures and the advantages brought forth by the use of composites.