Much like the bones in our bodies, the cytoskeleton consisting of filamentous proteins largely determines the mechanical response and stability of cells. These biopolymers form fiber networks, whose mechanical stability relies on the fibers’ bending resistance, in contrast to rubbers that are governed by entropic stretching of polymer segments. Thus, the elastic and dynamic properties of such semi-flexible polymers are very different from conventional polymeric materials. We describe recent advances both in theoretical modeling of such networks, as well as experiments on reconstituted in vitro acto-myosin networks and living cells. We show that such networks exhibit rich nonlinear and critical behavior. Unlike passive materials, however, living cells are kept far out of equilibrium by metabolic processes and energy-consuming molecular motors that generate forces to drive the machinery behind various cellular processes. We show how such internal force generation by motors can lead to dramatic mechanical effects, including a strong stiffening of cytoskeletal networks. Furthermore, stochastic motor activity can give rise to diffusive-like motion in elastic networks, as has been observed in living cells.