A system can be pushed beyond equilibrium through activity, resulting in remarkable system properties. In cytoskeletal networks, activity typically manifests itself through molecular motors, which transform chemical energy into mechanical work. In this thesis, we examine the relationship between activity and structure in cytoskeletal assemblies. First, we show that activity can be used as an indirect control for structure by modulating the rate at which the molecular motors do work. Additionally, we show that the activity of molecular motors improves the resilience of cytoskeletal assemblies to applied external forces. In non-biological systems, activity can be found in the form of time-correlated noise sources. We extend this physical concept of activity to generative diffusion models and show that time-correlated noise improves the performance of neural network learning and synthesis of novel samples. While activity results in remarkable system properties and emergent behaviors, it also presents new, unique challenges in developing the tools needed to study such systems. We overcome some of these challenges and develop new computational tools in order to explore the role of activity in two different contexts. Through our computational studies and theoretical considerations, we showcase and quantify how activity can enhance properties of systems ranging from cytoskeletal assemblies to generative diffusion models.