Exposure to mechanical stresses is a normal part of physiology for cells and tissues. Consequently, maintaining mechanical properties that give cells and tissues a combination of strength and durability is critical for their proper function. This is most apparent in diseased states, where genetic mutations to cytoskeletal and intercellular adhesion proteins alter mechanical properties and result in phenomena associated with cell and tissue mechanical failure. We have been developing new experimental tools for characterizing cell and tissue rheology at the millimeter and micron scale are providing new biophysical insights into this unique form of active matter. These properties can be traced to the nanometer scale, and I will present recent work that has uncovered how proteins associated with the actin cytoskeleton and intercellular adhesions dynamically organize into distinct structures that underly cell and tissue mechanical properties. This combination of experimental tools and analytical techniques from engineering and the physical sciences, with classical molecular biology and biochemistry, is now poised to enable a fundamental understanding of cell mechanics that is rich in complex biophysical phenomena and will guide novel therapeutic strategies.