Hydrogels are a promising and attractive option as polymeric gel networks, which have immensely fascinated researchers across the globe because of their outstanding characteristics such as elevated swellability, the permeability of oxygen at a high rate, good biocompatibility, easy loading, and drug release. Hydrogels have been extensively used for several purposes in the biomedical sector using versatile polymers of synthetic and natural origin. This review focuses on functional polymeric materials for the fabrication of hydrogels, evaluation of different parameters of biocompatibility and stability, and their application as carriers for drugs delivery, tissue engineering and other therapeutic purposes. The outcome of various studies on the use of hydrogels in different segments and how they have been appropriately altered in numerous ways to attain the desired targeted delivery of therapeutic agents is summarized. Patents and clinical trials conducted on hydrogel-based products, along with scale-up translation, are also mentioned in detail. Finally, the potential of the hydrogel in the biomedical sector is discussed, along with its further possibilities for improvement for the development of sophisticated smart hydrogels with pivotal biomedical functions.