Current commercial batteries cannot meet the requirements of next-generation technologies, meaning that the creation of new high-performance batteries at low cost is essential for the electrification of transport and large-scale energy storage. Solid-state batteries are being widely anticipated to lead to a step improvement in the performance and safety of batteries and their success is heavily dependent on the discovery, design and optimisation of the solid electrolytes that they are based on. In recent years, Li- and Na-rich anti-perovskite solid electrolytes have risen to become highly promising candidate materials for solid-state batteries on the basis of their high ionic conductivity, wide electrochemical window, stability, low cost and structural diversity. This perspective highlights experimental and atomistic modelling progress currently being made for Li- and Na-rich anti-perovskite solid electrolytes. We focus on several critical areas of interest in these materials, including synthesisability, structure, ion transport mechanisms, anion rotation, interfaces and their compatibility with anti-perovskite cathodes for the possible formation of anti-perovskite electrolyte- and cathode-based solid-state batteries. The opportunities and challenges for the design and utilisation of these materials in state-of-the-art solid-state batteries are also discussed. As featured throughout this perspective, the versatility, diversity and performance of anti-perovskite solid electrolytes make them one of the most important materials families currently under consideration for solid-state batteries.