There has been strong interest in high entropy alloys, formed of near-equiatomic mixtures of four or more elements. These materials challenge conventional thinking about alloys, with many compositions forming simple, single-phase materials. Prediction in these materials is challenging, due to the role of both composition, enthalpy and entropy, and the difficulty of examining the large number of competing possibilities. We demonstrate that information from high-throughput calculations can be utilized to predict both single-phase materials, as well as phase evolution in Al-containing materials. The latter undergo multiple transformations, and the theoretical predictions on these are remarkably close to experimental observations (diffraction and in situ microscopy) without fitting or input from experiment. The Al-containing materials form an interesting and controllable fine microstructure, with coherent interfaces. The ability to model the evolution such complex behavior without experimental input demonstrates that, with reasonable physical assumptions, a connection between atomistic, first-principles calculations and microstructure evolution is achievable even for complex alloys.