Smart biomaterials have significantly impacted human healthcare by advancing the development of medical devices designed to function within human tissue, mimicking the behavior of natural tissues. While the intelligence of biomaterials has evolved from inert to active over the past few decades, smart biomaterials take this a step further by making their surfaces or bulk respond based on interactions with surrounding tissues, imparting outcomes similar to natural tissue functions. This interaction with the surrounding tissue helps in creating stimuli-responsive biomaterials, which can be useful in tissue engineering, regenerative medicine, autonomous drug delivery, orthopedics, and much more. Traditionally, material engineering focused on refining the static properties of biomaterials to accommodate them within the body without evoking an immune response, which was a major obstacle to their unrestricted operation. This review highlights and explains various engineering approaches currently under research for developing stimuli-responsive biomaterials that tune their outcomes based on responses to bodily factors like temperature, pH, and ion concentration or external factors like magnetism, light, and conductivity. Applications in soft and hard tissue engineering, 4D printing, and scaffold design are also discussed. The advanced application of microfluidics, like organ-on-a-chip models, extensively benefits from the intrinsic smart properties of biomaterials, which are also discussed below. The review further elaborates on how smart biomaterial engineering could revolutionize biosensor applications, thereby improving patient care quality. We delineate the limitations and key challenges associated with biomaterials, providing insights into the path forward and outlining future directions for developing next-generation biomaterials that will facilitate clinical translation.