High-entropy alloys (HEAs) have emerged as a transformative class of materials distinguished by their complex chemical compositions, unique microstructures, and remarkable mechanical and functional properties. Traditionally, the discovery and optimization of HEAs have relied on conventional methods, including trial-and-error experimentation, first-principles calculations, molecular dynamics (MD), and CALculation of PHAse Diagrams (CALPHAD). Although these techniques have contributed immensely to the discovery of HEAs, they struggle to efficiently and accurately navigate the vast and complex compositional space of HEAs owing to their inherent limitations. This review presents the evolution of HEA design methodologies, with a key focus on the paradigm shift brought about by the integration of machine learning (ML) into the HEA discovery process. It unifies composition design, phase prediction, microstructure analysis, and property/process optimization within a single coherent framework. In addition, frontier developments, such as the generative adversarial network (GAN)-based data augmentation to tackle the issue of limited datasets, active learning loops for targeted experimentation, and hybrid ML-physics models that incorporate fundamental strengthening mechanisms, are emphasized. Efforts to address persistent challenges include the use of local interpretable model-agnostic explanation (LIME) and SHapley Additive exPlanations (SHAP), alongside physics-informed approaches, to improve model interpretability, whereas Bayesian-based techniques are utilized to improve uncertainty quantification. The synergy between experimental, computational, and data-driven approaches is highlighted as a key driver for creating predictive alloy-design frameworks that are both efficient and physically interpretable. By bridging conventional and data-driven approaches, this study not only deepens the understanding of HEA design principles but also outlines how emerging ML strategies are poised to accelerate the transition from material conception to application. An outlook on next-generation ML-driven HEA design is presented, with an emphasis on addressing current limitations and leveraging recent breakthroughs to expand the frontiers of material discovery.