Ab initio calculations, combined with experiment and longer length scale modeling, provides critical information on the stabilization of particular phases and microstructures. This talk will focus on approaches for connecting these issues for high entropy alloys (HEAs). These alloys pose new questions concerning the ability to predict single phase materials in alloys with a large number of components, particularly metastable phases. High-throughput calculations provide important predictive information as to which compositions may form single-phase solid solutions, including those where Hume-Rothery considerations have been shown to be inadequate. Effective Monte Carlo models of Al-containing HEAs show a complex set of phase transformations. These same materials exhibit unusual mechanical properties, including the unusual combination of increased strength and ductility when cooled. The materials challenge traditional considerations of solid-solution hardening, and atomistic simulations may provide critical insight into these processes. Work has been supported by the US DOE Office of Science, BES-MSED.