The cytoskeleton is the fundamental machinery that determines the morphology and mechanical properties of most eukaryotic cells. It is a complex network that is constituted of semiflexible polymer proteins. Its structure is regulated by various binding proteins that crosslink together several different filamentous polymers. The cytoskeletal scaffold is constantly influenced and agitated by three superfamilies of molecular motors that are called myosins, kinesins and dyneins. These motors are enzymes that convert the chemical free-energy released from the hydrolysis of ATP into mechanical work and directed locomotion. This thesis extends earlier theoretical framework based on the kinetic Master equations to capture both the passive Brownian motion of the network constituents and active chemical processes that occur in the cytoskeleton assemblies. This improved theory also enables us quantitatively to study the dynamical evolution of the probability distribution in the high dimensional configuration space of the network using a perturbation approximation around the thermal equilibrium. The mesoscale size of the nonequilibrium cytoskeletal assemblies demands the incorporation of the hydrodynamic coupling of the chemical shot noise arising from motorization into the theoretical framework to understand correctly the impact of coupled active diffusion on the dynamics of the far-from-equilibrium cytoskeleton. We find that hydrodynamic coupling is not only important for triggering the directed motion of the motors at single molecular level, but also rewrites the long-wavelength effective steady state that is characterized by an effective Fokker-Planck equation describing the enhanced anisotropic diffusion. The analytical theory also reveals mechanical heterogeneity associated with the motorized cytoskeleton at moderate level of motor agitation and succeeds in capturing the mechanically distorted phase that is stabilized by motorization. These results are confirmed by kinetic Monte Carlo simulations. The thesis also puts forth we derived two simple yet powerful one dimensional models to study the cellular contractility and motility, where the directionality biases of motor stepping are highlighted. The simulation results agree well with the theoretical predictions and they also boost our confidence on these simply building blocks to understand the cellular contractility and motility in higher dimensions.