Living cells can sense mechanical forces and convert them into biological responses. Similarly, biological and biochemical signals are known to influence the abilities of cells to sense, generate and bear mechanical forces. Studies into the mechanics of single cells, subcellular components and biological molecules have rapidly evolved during the past decade with significant implications for biotechnology and human health. This progress has been facilitated by new capabilities for measuring forces and displacements with piconewton and nanometre resolutions, respectively, and by improvements in bio-imaging. Details of mechanical, chemical and biological interactions in cells remain elusive. However, the mechanical deformation of proteins and nucleic acids may provide key insights for understanding the changes in cellular structure, response and function under force, and offer new opportunities for the diagnosis and treatment of disease. This review discusses some basic features of the deformation of single cells and biomolecules, and examines opportunities for further research.