Many studies suggest that naturally-occurring layered clay minerals can be used as a class of biocompatible solid supports for immobilizing enzymes. The corresponding clay mineral enzyme hybrids prove to have great potentials in catalysis and biosensing. This article reviews latest advances in using clay minerals as supports for the immobilization of enzymes. The immobilization of enzyme onto clay minerals can be made via non-covalent adsorption and covalent bonding. The non-covalent immobilization involves van der Waals forces, electrostatic interactions, hydrogen bonding, and hydrophobic interactions. For avoiding desorption of enzymes, immobilization can be conducted through direct covalent bonding between enzymes and clay minerals. Organic modification of clay minerals and addition of linking molecules are made to improve the immobilization so as to increase the loading, activity and stability of enzymes. Regarding the applications of enzyme immobilized on clay minerals, recent studies are made mainly in biocatalytic processes and in biosensors. For manufacturing biosensing electrodes, clay minerals with metal nanoparticles, graphene and carbon nanotubes prove to be more effective owing mainly to the enhanced electron transfer. Future work on clay mineral enzyme hybrids could lie in integrating more additional functional materials with clay mineral enzyme hybrids to build hierarchical structured catalysts and electrodes.