Hydrogels are hydrated three-dimensional polymeric networks with biomedical potential because they can encapsulate therapeutic agents and provide localised, sustained, or stimulus-responsive drug delivery. Their performance is determined by interacting variables, including polymer composition, synthesis route, crosslinking chemistry, drug loading, swelling, degradation, and the biological microenvironment. This multidimensional design space often makes hydrogel development slow and dependent on trial-and-error experimentation. This review examines the data-driven development of biomedical hydrogels for controlled drug delivery, focusing on clinical applications and emerging machine-learning approaches that support material selection, formulation design, synthesis optimisation, and release prediction. The review first discusses natural and synthetic hydrogels, including alginate, chitosan, gelatin-based systems, hyaluronic acid, and polyethylene glycol, with emphasis on how their physicochemical properties influence biocompatibility, synthesis flexibility, and drug-release behaviour. Key applications are then considered, including wound healing, cancer therapy, glucose-responsive insulin delivery, and inflammatory disease management. Particular attention is given to injectable and stimuli-responsive hydrogels, where formulation conditions and synthesis parameters can be tuned to improve localisation, therapeutic exposure, and release control. The review evaluates machine-learning methods, including random forest, gradient boosting, artificial neural networks, Gaussian process regression, and active learning, for predicting hydrogel properties, modelling release profiles, optimizing synthesis and formulation variables, and prioritizing experimental candidates. Finally, translational challenges are addressed, including small non-standardised datasets, limited external validation, weak in vitro-clinical correlations, material safety, explainability, reproducibility, scalability, and regulatory requirements. By integrating clinical, materials, synthesis, and machine-learning perspectives, this review highlights opportunities for developing safer and clinically relevant hydrogel-based drug-delivery systems.