Predicting the emergent behavior of the electrolytes and electrodes at their interfaces is crucial for the design of optimal energy storage materials for lithium-sulfur (Li-S) battery applications. For example, understanding lithium polysulfide solvation and diffusion in different solvent mixtures can help us predict the polysulfide dissolution mechanism and subsequently lead to the design of optimal electrolytes. To unravel the emergent behaviors of complex electrolyte systems, we have employed multi-nuclear and pulsed-field gradient (PFG) NMR experiments, obtaining a molecular level understanding of the solution structure and translational dynamics of ions/solvents within Li-S battery electrolytes. Based on this understanding, we proceed to study electrode-electrolyte interfacial process such as the formation of solid-electrolyte interphase (SEI) layers. Metal anodes under various electrochemical conditions were analyzed using multi-nuclear solid-sate NMR spectroscopy to understand ion nucleation (dendrite growth) and reactivity (SEI layer formation) on the electrode surface. Finally, we correlate the NMR-derived local structure to emergent behaviors of electrolyte and electrode-electrolyte interfacial process to gain a comprehensive multiscale understanding of Li-S electrochemistry during charge/discharge processes.