MAX phases, a family of ternary layered carbide and nitride compounds characterized by their atomic-scale hybridization of metallic and covalent-ionic bonding, have emerged as potential materials for extreme environments, including fusion reactor cladding and ultrahigh-temperature sensing. Despite a twofold increase in known compositions over the past five years, the discovery and application of novel MAX phases remain hindered by metastable phase competition under non-equilibrium synthesis, inefficiencies in experimental synthesis/characterization, and ambiguous performance metrics under extreme conditions (e.g., high temperatures, irradiation). Recent breakthroughs in computational materials science — notably high-throughput density functional theory (HT-DFT) and machine learning (ML) — have revolutionized the exploration of these materials by enabling predictive screening of stability and performance. This review systematically analyzes advances in theoretical understanding of MAX phases, focusing on three pillars: electronic structure, thermodynamics and irradiation performance. Finally, brief insights into the challenges and future opportunities for the MAX phases are provided.