Basic concepts in physical chemistry are taught and understood on the molecular level. Only recently, single-molecule experiments make it possible to detect and monitor dynamic trajectories of individual molecules. To understand these measurements, we focus on two conceptual issues: (i) the nature of the information content of single molecule data and how to best represent this information with mathematically rigorous and physically meaningful models and (ii) the signatures of non-equilibrium steady-states in kinetic networks of enzymatic reactions and in driven processes. In this general area, we also study indicator analyses of conformational fluctuations, Bayesian statistical algorithms for processing single molecule data, and first-principle calculations of single polymer dynamics.