Abstract <p>This review highlights the essential role of adsorption in CO₂ capture, H₂ and methane storage, demonstrating their significance in environmental and energy applications. Effective modeling and simulation are important for optimizing these processes, enabling improved system design, performance prediction, and overall efficiency. The study provides a comprehensive review of key mathematical and empirical models, including diffusion and adsorption-controlled kinetics, as well as isotherms such as Langmuir, Freundlich, and BET. Advanced models like Sips and Dubinin–Radushkevich, applied to CO₂/H₂ separation and biogas purification, are also discussed. Nonlinear regression is identified as more accurate than linear methods, while artificial neural networks (ANNs) and response surface methodology (RSM) offer superior capabilities in handling complex variables. These advanced modeling approaches are essential for enhancing adsorption system performance, with significant implications for scaling up in environmental and energy-related applications.</p> Graphical Abstract <p></p>