Cytokinesis is the mechanical process that allows the simplest unit of life, the cell, to divide, propagating itself. To divide, the cell converts chemical energy into mechanical energy to produce force. This process is thought to be active, due in large part to the mechanochemistry of the myosin-II ATPase. The cell's viscoelasticity defines the context and perhaps the magnitude of the forces that are required for cytokinesis. The viscoelasticity may also guide the force-generating apparatus, specifying the cell shape change that results. Genetic, biochemical, and mechanical measurements are providing a quantitative view of how real proteins control this essential life process.