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The accelerating climate crisis, driven by annual CO₂ emissions exceeding 37 billion metric tons, necessitates the rapid advancement of Carbon Capture and Storage (CCS) and Direct Air Capture (DAC) technologies. Metal–Organic Frameworks (MOFs) have emerged as highly promising sorbents due to their tunable pore architectures and exceptional surface areas; however, exploration of their vast chemical design space remains computationally prohibitive. This review systematically examines the expanding role of Machine Learning (ML) in accelerating CO₂ capture research within MOFs. Using a structured evaluation protocol, we assess state-of-the-art models across four key dimensions: predictive performance, descriptor physical relevance, mechanistic interpretability, and process-level applicability. Recent advances in Machine Learning Interatomic Potentials (MLPs) demonstrate that framework flexibility significantly influences adsorption thermodynamics and diffusivity, challenging conventional rigid-lattice assumptions. Generative approaches—including Deep Reinforcement Learning and transformer-based architectures—enable inverse design of high affinity frameworks, while physics-informed descriptor engineering improves predictive accuracy across pressure regimes (R² > 0.90). Importantly, the field is transitioning from isolated property prediction toward multiscale, process-integrated optimization, where ML models couple material features with industrial performance metrics such as CO₂ purity and recovery in pressure swing adsorption systems. Collectively, these developments indicate that future progress will depend on physics informed, interpretable architectures capable of bridging molecular-scale discovery with experimentally robust and water-stable materials suitable for industrial deployment.