Living systems, as well as most physical systems with promise in industry, technology and medicine, operate outside of thermodynamic equilibrium. While there exists a precise theoretical framework called statistical mechanics to treat equilibrium systems, there is no equivalent theory for out-of-equilibrium systems, making the discovery of principles that dictate nonequilibrium phenomena of crucial importance. The search for principles to better understand non-equilibrium dynamics often starts with a quest to understand energy dissipation, the amount of energy consumed due to non-conservative forces acting on the system. In this dissertation I look at several systems that display a variety of non-equilibrium behaviors in order to understand how energy dissipated by nonconservative forces applied at the microscopic level affects macroscopic properties. This dissertation contains three major chapters, each one containing derivations of new nonequilibrium statistical mechanics results, followed by proof of principle experiments that show how the analytical work could be used to garner novel understanding. First, concepts from stochastic thermodynamics and liquid state theories are used to study the relationship between energy dissipation and changes in the structural properties of a minimal model of a liquid driven by external rotating forces. As a proof of principle, a model system of a particle diffusing in a fluctuating energy landscape under a force that has a non-conservative component is considered. This model is used to draw insight into how nonequilibrium forcing as well as a changing conservative force landscape felt by an active particle can affect its diffusion and lead to phase transitions. Second, explicit coarse-graining and stochastic calculus are used to obtain more precise, quantitative relationships between energy dissipation, density correlations and diffusion in generic nonequilibrium liquids, a class that the fluid in part one belongs to. As a proof of principle, large-deviation biased ensembles are considered, where trajectories are steered in a way that mimics the effects of an external drive. The choice of the biasing function is informed by the aforementioned relationship between dissipation and density correlations. Using analytical and computational techniques, it is shown that the choice of biasing effectively renormalizes interactions in a controlled manner. Third, a mean-field framework to connect energy dissipation and structure is constructed. Unlike most existing approaches, this framework is applicable even for nonequilibrium liquids with strong interactions. The theory reveals a robust analytical relation between dissipation and density correlations. As a proof of principle, these results are further used to construct a neural network which maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Altogether, these results add significant contributions to the small pool of existing analytical and theoretical expressions to describe nonequilibrium systems. Furthermore, through proof of principle experiments inspired by these analytical results, this work provides novel perspectives on the interplay between dissipation and the structure, transport and function of liquids and soft materials.