High-entropy alloys (HEAs), and in particular, refractory HEAs (RHEAs), can offer remarkable thermomechanical properties, corrosion tolerance, and irradiation tolerance, making them candidates for structural materials in extreme environments such as advanced nuclear applications. Despite their apparent potential, the current understanding of the irradiation tolerance of RHEAs and their suitability for such nuclear applications is limited. This dissertation provides an in-depth study into the irradiation response of these alloys, and the mechanisms behind their radiation resistance, and further explores the potential of RHEAs in nuclear applications through material design and optimisation. The first part of this research focusses on the TiZrNbHfTa RHEA – primarily in its nanocrystalline (NC) state – irradiated under conditions representative of advanced nuclear applications. The alloy demonstrated excellent microstructural stability and retained essential mechanical properties post-irradiation, with significantly less hardening compared to traditional alloys irradiated under like conditions. The research then explores the unique mechanisms intrinsic to HEAs, such as high configurational entropy, severe lattice distortion, and sluggish diffusion, clarifying how such mechanisms may improve the irradiation tolerance of RHEAs. However, the research also highlights the sensitivity of RHEAs to phase constitution, with the introduction of additional gregation affecting the alloys’ response to irradiation. Furthermore, the competitive viability of HEAs against existing nuclear structural materials is explored, focussing on potential applications where HEAs could provide superior performance. To foster the development of such alloys, nuclear-relevant property calculations and a framework for alloy design is proposed. A novel RHEA, Ti55Zr30Ta6V5Cr2Fe2 (Ti55), was synthesised and tested, designed with an aim to minimise neutron capture cross section, transmutation losses, and gamma activity. The novel alloy exhibited promising mechanical properties which provide motivation for further material development. This doctoral dissertation significantly contributes to the field of RHEAs for advanced nuclear applications. It offers insights into their behaviours under irradiation and provides guidelines for their design and optimisation. With continued exploration and refinement, the vast potential of RHEAs can be harnessed, potentially addressing materials challenges in the field of nuclear materials.