Hydrogen is widely regarded as a cornerstone energy carrier for achieving net-zero emissions; however, its combustion in conventional air-based engines inevitably leads to nitrogen oxide formation due to high-temperature reactions between oxygen and nitrogen. The hydrogen-argon power cycle (H₂-APC) replaces nitrogen with argon as the working fluid to fundamentally decouple combustion from both carbon and nitrogen chemistry. This carbon- and nitrogen-free combustion concept enables intrinsically zero emission, while simultaneously enhancing thermal efficiency owing to argon's high specific heat ratio and inert thermophysical properties. This review provides a comprehensive and critical assessment of the current state of H₂-APC research, including thermodynamic cycle analysis, combustion kinetics, mixing dynamics, flame stabilization, and abnormal combustion phenomena. Both numerical modelling and experimental demonstrations are systematically reviewed. The analysis highlights key advantages of H₂-APC operation, including elevated efficiency limits, extended ultra-lean combustion regimes, and suppressed pollutant formation. At the same time, the review identifies major technical and system-level challenges, notably improved abnormal combustion, argon supply and recycling, cost and infrastructure constraints. To address the challenges, mitigation strategies such as water injection, pre-chamber and advanced ignition concepts, and closed-loop argon recycling architectures are critically discussed. Finally, the review outlines future research priorities, including high-fidelity optical diagnostics, validated kinetic and turbulence-chemistry interaction models, and integrated techno-economic and life-cycle assessments. Overall, the H₂-APC represents a transformative pathway for sustainable power generation and propulsion, positioning zero-emission internal combustion engines as a viable complement to renewable and electrified energy systems.