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High-entropy alloys (HEAs) exhibit exceptional structural and functional properties arising from their complex local chemical environments, and their vast compositional space offers considerable flexibility to further tune and optimize these properties. Atomistic simulations based on density functional theory (DFT) have played a central role in elucidating the thermodynamic, mechanical, magnetic, and defect-related properties of HEAs. However, DFT simulations are severely limited by the intrinsic chemical and configurational complexity of these alloys, particularly because reliable predictions require extensive statistical sampling over chemically diverse configurations and access to extended spatial and temporal scales. In this review, we summarize recent advances in atomistic simulations of HEAs, with particular emphasis on machine learning interatomic potentials (MLIPs), which extend beyond conventional DFT approaches. We discuss how MLIPs enable statistically robust simulations with near-DFT accuracy while dramatically reducing computational cost, thereby allowing explicit treatment of chemical short-range order, vibrational contributions to Gibbs energies, point defects, diffusion, dislocation behavior, grain boundaries, and hydrogen absorption in chemically complex alloys. Particular attention is devoted to the role of local chemical environments, many-body interactions, and configurational sampling in determining HEA properties. We further review recent developments in universal/foundation MLIPs trained on chemically diverse datasets and discuss their potential for rapid and transferable atomistic simulations of HEAs across broad compositional and configurational spaces. We discuss current limitations and open challenges, including transferability to highly distorted defect configurations, treatment of magnetic and charge degrees of freedom, incorporation of finite-temperature excitations, and construction of representative training datasets for chemically and structurally complex systems. This review aims to provide a comprehensive perspective on the ongoing transition from conventional DFT-based simulations toward scalable, statistically rigorous, and predictive atomistic modeling frameworks for HEAs and related compositionally complex materials.