Thermodynamic equilibrium is a strong constraint on the statistics of physical systems that has led to a correspondingly powerful theory, equilibrium statistical mechanics, that connects microscopic forces to macroscopic properties. Experiments now confirm the longstanding speculation that living systems can be fruitfully modeled using physical principles, and the challenge is to develop statistical mechanics for such systems, which violate thermodynamic equilibrium. Progress in nonequilibrium statistical mechanics has been made by focusing on energy dissipation, the amount of energy consumed via currents of work and heat. In this dissertation I look at energy dissipation in two systems displaying fundamentally nonequilibrium collective behavior in order to understand, quantitatively and qualitatively, how nonequilibrium driving produces this behavior. First, I explore the relation between dissipation and changes in the structure and transport properties of a minimal, chiral driven liquid that undergoes nonequilibrium phase separation. The model mimics recent experiments that use an external magnetic field to reversibly break symmetry and phase separate liquids of colloidal particles. These and other similar experiments are in turn broadly inspired by biological "active matter'" systems such as bacterial swarms. Using concepts from stochastic thermodynamics and liquid state theories, I show how the work performed on the system by various nonconservative, time-dependent forces---which represents the nontrivial contribution to the energy dissipation---modifies the force fluctuations and diffusion of the liquid, leading to phase separation. I then characterize interfaces in the phase-separated state, showing that they exhibit fluctuations unlike those seen in equilibrium systems. Second, I explore how energy dissipation enables precise timing in minimal Markov state models of biological clocks known generically as biochemical oscillators. These oscillators are ubiquitous in biology and allow organisms to properly time their biological functions. Using a transfer matrix perturbation theory, I obtain analytical expressions for the coherence and period of oscillations in single-cycle Markov models that reveal that higher energy dissipation enables higher precision of both quantities among a population of oscillators with randomly distributed rates. I then develop a mapping based on first passage time distribution between models with multiple small cycles and single-cycle models. The mapping allows the analytical theory to be extended to multi-cycle oscillators, revealing that energy dissipation also enables robust timing among a population of oscillators with different topologies. The case studies presented here demonstrate how energy dissipation enables precise and adaptive collective behavior in nonequilibrium systems.