Enzymes are important biomarkers for molecular diagnostics and targets for the action of drugs. In turn, inorganic nanoparticles (NPs) are of interest as materials for biological assays, biosensors, cellular and in vivo imaging probes, and vectors for drug delivery and theranostics. So how does an enzyme interact with a NP, and what are the outcomes of multivalent conjugation of its substrate to a NP? This invited feature article addresses the current state of the art in answering this question. Using gold nanoparticles (Au NPs) and semiconductor quantum dots (QDs) as illustrative materials, we discuss aspects of enzyme structure-function and the properties of NP interfaces and surface chemistry that determine enzyme-NP interactions. These aspects render the substrate-on-NP configurations far more complex and heterogeneous than the conventional turnover of discrete substrate molecules in bulk solution. Special attention is also given to the limitations of a standard kinetic analysis of the enzymatic turnover of these configurations, the need for a well-defined model of turnover, and whether a "hopping" model can account for behaviors such as the apparent acceleration of enzyme activity. A detailed and predictive understanding of how enzymes turn over multivalent NP-substrate conjugates will require a convergence of many concepts and tools from biochemistry, materials, and interface science. In turn, this understanding will help to enable rational, optimized, and value-added designs of NP bioconjugates for biomedical and clinical applications.