Anaerobic digestion (AD) is a widely recognized method for converting organic waste into biogas, offering a sustainable solution for both waste management and renewable energy generation. This review critically examines recent advancements in mathematical modeling and machine learning (ML) approaches applied to biogas production from AD processes. The study categorizes the models into daily and cumulative biogas production models, kinetic models, and hybrid AI-based predictive techniques. Special attention is given to the comparative evaluation of first-order kinetics, modified Gompertz, and Chen-Hashimoto models, highlighting their applicability and limitations. Furthermore, the integration of artificial neural networks (ANNs) and other ML algorithms is discussed in the context of optimizing biogas yield, understanding system dynamics, and reducing operational uncertainties. Research gaps are identified, including the need for more robust hybrid models, real-time monitoring systems, and studies under diverse feedstock and environmental conditions. The review emphasizes that combining traditional modeling with intelligent systems offers a powerful approach to enhancing AD performance and scaling sustainable energy solutions.