The actin cortex is a thin polymer network beneath the plasma membrane in animal cells. It acts as a mechanical shield of the cell and as a major regulator of cell shape and cell migration. The actin cortex is a complex material with time-dependent viscoelastic mechanical properties. It is further subject to a self-generated active contractile stress and to constituent turnover. I will discuss our measurement results on frequency-dependent cortical viscoelasticity measured by atomic force microscopy. In addition, I will discuss how mechanosensitivity of molecular bonds can affect molecular composition of the cortex and how this mechanosensitivity can be quantified in live cells.