Materials used in high temperature applications are carefully engineered to achieve optimal mechanical properties and chemical durability. Refractory alloys comprising elements from groups four,five and six of the periodic table are an emerging class of high-temperature materials that promise high strength and high thermal stability. However, relationships between alloy chemistry, processing strategies and material properties remain unclear. In this talk I will highlight recent advances in computational materials science that enable the rigorous and rational design of high-performance engineering alloys. First-principles calculations will be used with machine-learning and statistical mechanics techniques to rigorously describe the thermodynamic and kinetic properties of multicomponent refractory alloys. High-throughput calculations will be employed to discern design rules for the formation of single phase multi-principal element refractory alloys. Diffusion mechanisms and phase transformations in multicomponent refractory alloys will also be highlighted. The techniques and results presented in this talk provide important insights for the design of advanced structural alloys.