High-entropy alloys (HEAs) extend alloy design beyond conventional solvent-based systems into vast multicomponent compositional spaces, enabling unusual combinations of structural and functional properties. This review connects the physical metallurgy of HEAs with the data-driven approaches increasingly used to accelerate their design and discovery. First, the thermodynamic and kinetic foundations of HEAs are examined, including configurational entropy, lattice distortion, diffusion behavior, and synergistic elemental interactions, while also considering the limitations of the classical core-effect framework. Liquid-state, solid-state, vapor-state, and emerging synthesis routes are then reviewed, with emphasis on how processing controls phase formation, chemical homogeneity, microstructure, defects, and contamination. The resulting mechanical, corrosion, thermal, electrical, and magnetic properties are discussed through processing–structure–property relationships. The second part evaluates artificial-intelligence and machine-learning approaches for phase classification, property prediction, interpretable modeling, active learning, Bayesian optimization, CALPHAD-assisted screening, and machine-learned interatomic potentials. Particular attention is given to the ability of these methods to reduce the experimental burden associated with the enormous HEA design space, as well as to persistent challenges involving data scarcity, class imbalance, inconsistent measurements, and inadequate representation of processing history and microstructure. Finally, emerging opportunities in transfer learning, generative models, physics-informed learning, and self-driving laboratories are discussed. By integrating physical metallurgy with data-driven design, this review provides a unified perspective on the transition from empirical alloy development toward accelerated HEA discovery.