Studies of biological systems and materials, together with recent experimental and theoretical advances in colloidal and nanoscale materials, have shown how nonequilibrium forcing can be used to modulate organization in many novel ways. In this review, we focus on how an accounting of energy dissipation, using the tools of stochastic thermodynamics, can constrain and provide intuition for the correlations and configurations that emerge in a nonequilibrium process. We anticipate that the frameworks reviewed here can provide a starting point to address some of the unique phenomenology seen in biophysical systems and potentially replicate them in synthetic materials.