<p>Refractory high-entropy alloys (RHEAs) comprising multiple high-melting point elements have been proposed as replacements for Ni-based superalloys. Here, we critically assess the research performed on RHEAs, provide perspectives on their salient features, and suggest directions for future research to fill gaps in current knowledge. We conclude that single-phase RHEAs are either too weak in creep at high temperatures or too brittle at low homologous temperatures to make them viable replacements for Ni-based superalloys. Precipitates can potentially enhance creep strength but only if their solvus temperatures are higher than the operating temperatures of superalloys, which rules out those reliant on Al additions. Ru-containing precipitates have high solvus temperatures but there is essentially no information about their mechanical properties, so further studies are needed to evaluate their potential. Research is also needed to understand the strength–ductility/toughness tradeoff in the presence of precipitates, and the constraints imposed by the poor oxidation resistance of RHEAs.&#xa0;In the two main classes of single-phase RHEAs, improving the room-temperature ductility of V-Nb-Ta-Mo-W alloys should be a priority but attempts at further improving the room-temperature ductility of Ti-Zr-Hf-Nb-Ta alloys seems misguided as they currently have adequate ductility.</p> Graphical abstract <p></p>