The behaviors and functions of individual cells, fundamental to the complexity of multicellular organisms, are regulated by their integrated response to a variety of environmental cues such as soluble factors, extracellular matrix (ECM)-mediated signals, and cell-cell interactions. Among these cues, the biomechanical feature of the ECM, represented by its elasticity, has been increasingly recognized as a dominating factor of cell fate. This review article aims to provide an overview of the general principles and recent advances in the field of matrix elasticity-dependent regulation of cellular activities and functions, the underlying biomechanical and molecular mechanisms, as well as pathophysiological implications. A discussion is also provided as to how material design strategies can be used to control the local microenvironment of stem cells to direct their lineage commitment and functions toward tissue development and regeneration.