The mechanical world we live in plays a major role in the physiology and pathology of cells and extracellular matrices (ECMs) of tissues in living organisms, and understanding how micromechanics change spatially through health and disease is key to developing new effective treatments. That being said, research on the micromechanics of cells and their microenvironments has been greatly outpaced by a biochemical understanding of these systems. This is in part because many of the mechanical properties of cells and tissues not only vary over space but also are difficult or impossible to measure with direct experimentation. In addition, the micromechanics of these systems are highly dependent on the 3D nature of tissues, and therefore methods for studying cellular micromechanics require a focus on 3D cell cultures. In the present chapter, cutting-edge techniques that couple 3D experimentation with computational modeling to overcome these previous limitations are reviewed. Examples are taken from heart valve interstitial cells and their microenvironment since heart valve tissue is highly mechanically active. These approaches can be applied to other 3D cell/hydrogel systems with minimal changes and allow for the determination of the spatially varying micromechanics of the ECM and cells from various phenotypic states.