Enzyme mimics or artificial enzymes are a class of catalysts that have been actively pursued for decades and have heralded much interest as potentially viable alternatives to natural enzymes. Aside from having catalytic activities similar to their natural counterparts, enzyme mimics have the desired advantages of tunable structures and catalytic efficiencies, excellent tolerance to experimental conditions, lower cost, and purely synthetic routes to their preparation. Although still in the midst of development, impressive advances have already been made. Enzyme mimics have shown immense potential in the catalysis of a wide range of chemical and biological reactions, the development of chemical and biological sensing and anti-biofouling systems, and the production of pharmaceuticals and clean fuels. This Review concerns the development of various types of enzyme mimics, namely polymeric and dendrimeric, supramolecular, nanoparticulate and proteinic enzyme mimics, with an emphasis on their synthesis, catalytic properties and technical applications. It provides an introduction to enzyme mimics and a comprehensive summary of the advances and current standings of their applications, and seeks to inspire researchers to perfect the design and synthesis of enzyme mimics and to tailor their functionality for a much wider range of applications.