Actomyosin-based cortical flow is a fundamental engine for cellular morphogenesis. Cortical flows are generated by cross-linked networks of actin filaments and myosin motors, in which active stress produced by motor activity is opposed by passive resistance to network deformation. Continuous flow requires local remodeling through crosslink unbinding and/or filament disassembly. But how local remodeling tunes stress production and dissipation, and how this in turn shapes long range flow, remains poorly understood. To address this question, I developed a computational model for cross-linked actomyosin networks based on minimal requirements for production and dissipation of contractile stress, namely asymmetric filament compliance, spatial heterogeneity of motor activity, reversible cross-links and filament turnover. Using this model, I characterized systematically how the production and dissipation of network stress each depend on network architecture, cross-link dynamics and filament turnover. Then I determined how these dependencies combine to determine overall rates of cortical flow. My analysis predicts that filament turnover plays two key roles in shaping cortical flow: First, it allows networks to maintain active stress at steady state against external resistance and second, it allows networks to continuously dissipate passive internal resistance to external force, while maintaining structural integrity. My model predicts that steady state stress increases with filament lifetime up to a characteristic time τa, then decreases with lifetime above τa; Effective viscosity increases with filament lifetime up to a characteristic time τc, and then becomes independent of filament lifetime and sharply dependent on crosslink dynamics. Finally, I show that these individual dependencies of active stress and effective viscosity define multiple regimes of steady state flow. In particular my model predicts the existence of a regime, where filament lifetimes are shorter than both τc and τa, in which dependencies of effective viscosity and steady state stress cancel one another, such that flow speed is insensitive to filament turnover. My model also predicts a simple dependence of flow velocity on molecular scale properties of motor activity and crosslink dynamics. In complementary work, in collaboration with other members of the Munro Lab, I developed methods to measure actin filament turnover in C. elegans embryos using single molecule imaging. Together, these results provide a framework for understanding how animal cells tune cortical flow through local control of network remodeling.