Abstract: Cells of higher organisms contain a dynamically remodeling filamentous network, called cytoskeleton, comprised of actin, myosin and many other molecules. The cytoskeletons endue cells with their instantaneous shapes, providing a machinery for cells to move around, generate forces and also integrate both chemical and mechanical signaling. In terms of the physico-chemical mechanisms, the underlying acto-myosin network growth and remodeling processes are based on a large number of chemical and mechanical interactions, which are mutually coupled, and spatially and temporally resolved. To investigate the fundamental principles behind the self-organization of these networks, we have developed a detailed physico-chemical, stochastic model (MEDYAN) of actin filament growth dynamics, where the mechanical rigidity of filaments and their corresponding deformations under internally and externally generated forces are taken into account. Our work sheds light on the interplay between the chemical and mechanical processes governing the cytoskeletal dynamics, in particular, the emergence of polarity alignment and contractility in these systems, and also highlights the importance of diffusional and active transport phenomena. Our simulations reveal how different acto-myosin micro-architectures emerge in response to varying the network composition, emphasizing the important interplay between actin treadmilling , molecular transport and myosin-induced filament rearrangements.