Cells are responsive to external cues in their environment telling them to proliferate or migrate within their surrounding tissue. Sensing of cues that are mechanical in nature, such stiffness of a tissue or forces transmitted from other cells, is believed to involve the cytoskeleton of a cell. The cytoskeleton is a complex network of proteins consisting of polymers that provide structural support, motor proteins that remodel these structures, and many others. We do not yet have a complete understanding of how cytoskeletal components respond to either internal or external mechanical force and stiffness. Such an understanding should involve mechanisms by which constituent molecules, such as motor proteins, are responsive to mechanics. Additionally, physical models of how forces are transmitted through biopolymer networks are necessary. My research has focused on networks formed by the cytoskeletal filament actin and the molecular motor protein myosin II. Actin filaments form networks and bundles that form a structural framework of the cell, and myosin II slides actin filaments. In this thesis, we show that stiffness of an elastic load that opposes myosin-generated actin sliding has a very sharp effect on the myosin force output in simulations. Secondly, we show that the stiffness and connectivity of cytoskeletal filaments regulates the contractility and anisotropy of network deformations that transmit force on material length scales. Together, these results have implications for predicting and interpreting the deformations and forces in biopolymeric active materials.