Mammalian cells control their shape and function by altering their mechanical properties through structural rearrangements and changes in molecular biochemistry at the nanometer scale. Yet, little is known about the molecular and biophysical basis of cell mechanics. Most of the existing engineering models of cells are ad hoc descriptions based on measurements obtained under particular experimental conditions, and these continuum models usually ignore contributions of subcellular structures and molecular components. More than 20 years ago, we introduced an alternative model of the cell based on tensegrity architecture which proposes that isometric tension in the cytoskeleton is critical for cell shape stability. Key to this model is the concept that this stabilizing tensile “prestress” results from a complementary force balance between multiple, discrete, molecular support elements, including microfilaments, intermediate filaments and microtubules in the cytoskeleton, as well as external adhesions to extracellular matrix and to neighboring cells.