Stimuli-responsive (smart) hydrogels have attracted widespread attention as biomimetic systems due to their ability to respond to subtle changes in external and internal stimuli ranging from physical triggers such as temperature and electric field to chemical triggers like glucose and pH. Besides their intriguing behavior, the main interest in such smart hydrogels lies in their potential industrial and biomedical applications. Some of these applications include injectable biomaterials, tunable surfaces for cell sheet engineering, sensors, and actuators. In this review, we discuss the fundamental principles underlying the stimuli-responsive behavior of hydrogels and how these properties have led to major technological innovations. We also review recent advancements in the field of hydrogels, including self-healing and stimuli-responsive degradation in hydrogels. We conclude by providing a perspective on the potential use of smart hydrogels as multifunctional, bioactuating systems for cell and tissue engineering.