The relationship between the structure of active matter systems and the driving forces which push them out of equilibrium at the level of individual particles is, in general, complex and highly system-dependent. For each system of interest, understanding this relationship is essential, both for tuning and manipulating a given active matter system to yield desired behaviors and properties, and for attempting to perceive universal principles which control and constrain the behavior of out-of-equilibrium systems more broadly. In this thesis, I describe theoretical and computational efforts to understand the structure-driving force relationship for two very different active matter systems. The first is a simple active fluid. Drawing on various tools from liquid state theory, I demonstrate that a robust connection exists between static pair correlations and the rate of dissipation of the energy added to the system by the driving forces. This connection is particularly convenient, as there is no need for dynamic information or higher-order structural features to accurately predict the dissipation, and the relationship holds both near and far from equilibrium conditions, as long as the active fluid remains a fluid. The second active matter system is an active solid, designed to have multiple distinct stable states: a square lattice configuration and a hexagonal lattice configuration. The relative stability of these states can be modulated solely by the changing the magnitude of driving forces being applied in the system, and it is possible under certain conditions to induce phase transitions. While the active solid under consideration is essentially a toy model, it is a useful demonstration of the ability of driving forces to control the structure of solids in potentially precise and functionally important ways.