Despite two decades of experimental studies on MAX phases, designing their optimal composition and microstructure has remained a challenge mainly because of the large number of possible compositions and microstructures, and a lack of robust physical models that relate their composition and microstructure to properties. The overall goal of this research program is to overcome those challenges and foster design of MAX phases for high temperature applications by: (1) developing physics-based predictors for the formation of protective alumina layers; (2) developing micromechanical models and identifying compositional/structural parameters that control intrinsic thermomechanical properties; (3) designing Bayesian calibration protocols for parameter identification; (4) implementing and deploying Efficient Global Optimization protocols for the efficient discovery of MAX phases with optimal thermomechanical properties and; (5) validating the proposed framework through material synthesis, characterization and thermomechanical testing. This will provide guiding fundamental knowledge and protocols to design optimal compositions and microstructures of the MAX phases for high temperature application.