Soft active systems are a new and exciting class of complex materials to which energy is continuously supplied by internal or external sources. Examples include bacterial swarms, vibrated granular matter and the cytoskeleton of eukaryotic cells. The latter is a complex dynamical network of long filamentary proteins that mediates important cellular functions, including cell motility, division and intracellular transport. It is maintained out of equilibrium by a variety of biochemical processes and the action of motor proteins that act like nanomachines, supplying energy to the filament network and continuously remodeling its structure. \par In this talk I will describe our recent work on developing theoretical models to describe the nonequilibrium dynamics of networks of cytoskeletal filaments and motor proteins. \par Activity drives athermal transitions between disordered and self-assembled ordered states and controls the emergence of complex spatial structures, similar to those seen {\it in vitro}. The remarkable effects of activity on the rheological properties of the network will also be discussed.