The concepts of bioinspiration and biomimetics that seek to elucidate the morphology and functions of living organisms and specific reactions within cells, and extraction of important elements from these concepts to design functional molecules and high-performance materials are becoming more and more widespread. This review summarizes the progress in research on hydrogels inspired by the stimuli-responsiveness of cell functions. For application to a self-regulated release system of insulin to regulate blood glucose levels, various polymer hydrogels have been designed using bioactive molecules such as enzymes and lectins to sense glucose concentrations. In addition, as a fully synthetic glucose-responsive hydrogel, a complex of a polymer having phenylboronic acid groups that form reversible bonds with sugars and a multivalent hydroxyl group polymer has been researched. This reversible hydrogel system can be further developed to act as an extracellular matrix in which cells can preferably reside. The proliferation and differentiation of encapsulated cells in hydrogels are controlled by reversible changes in the hydrogel properties in response to sugar. Another advantage is that cells can be safely retrieved by adding sugar to dissociate the hydrogel. These bioinspired polymer hydrogels can serve as important materials for the development of new medical technologies, such as the controlled release of bioactive molecules, regulated cell culture environmental matrices, and applications in layered and three-dimensional cell culture systems to create organized tissue structures.