Recent developments in computational cell and biomolecular mechanics have provided valuable insights into the mechanical properties of cells, subcellular components and biomolecules, while simultaneously complementing new experimental techniques used for deciphering the structure-function paradigm in living cells. These computational approaches have direct implications in understanding the state of human health and the progress of disease and can therefore aid immensely in the diagnosis and treatment of diseases. We provide an overview of the computational approaches that are currently used in understanding various aspects of cell and bimolecular mechanics. Our emphasis is on state-of-the-art techniques and the progress made in addressing key challenges in biomechanics.