Filamentous biopolymers such as F-actin, vimentin, fibrin and collagen that form networks within the cytoskeleton or the extracellular matrix have unusual rheological properties not present in most synthetic soft materials that are used as cell substrates or scaffolds for tissue engineering. Gels formed by purified filamentous biopolymers are often strain stiffening, with an elastic modulus that can increase an order of magnitude at moderate strains that are relevant to cell and tissue deformation in vivo. This review summarizes some experimental studies of non-linear rheology in biopolymer gels, discusses possible molecular mechanisms that account for strain stiffening, and explores the possible relevance of non-linear rheology to the interactions between cell and extracellular matrices.