Polymeric hydrogels are widely explored materials for biomedical applications. However, they have inherent limitations like poor resistance to stimuli and low mechanical strength. This drawback of hydrogels gave rise to ‘‘smart self-healing hydrogels’’ which autonomously repair themselves when ruptured or traumatized. It is superior in terms of durability and stability due to its capacity to reform its shape, injectability, and stretchability thereby regaining back the original mechanical property. This review focuses on various self-healing mechanisms (covalent and non-covalent interactions) of these hydrogels, methods used to evaluate their self-healing properties, and their applications in wound healing, drug delivery, cell encapsulation, and tissue engineering systems. Furthermore, composite materials are used to enhance the hydrogel’s mechanical properties. Hence, findings of research with various composite materials are briefly discussed in order to emphasize the healing capacity of such hydrogels. Additionally, various methods to evaluate the self-healing properties of hydrogels and their recent advancements towards 3D bioprinting are also reviewed. The review is concluded by proposing several pertinent challenges encountered at present as well as some prominent future perspectives.