This dissertation describes chemical compositions and fundamental mechanisms of formation of solid electrolyte interphase (SEI) layers on a graphite anode and a microporous carbon/sulfur cathode. Direct analysis on the authentic SEIs by solution NMR spectroscopy is combined with investigations on model chemical systems. We uncovered the presence of highly similar SEI components (i.e., lithium ethylene mono-carbonate, LEMC and lithium methyl carbonate, LMC) on the two types of electrodes, but the components are generated from completely different chemical routes. The solution and solid-state properties of the compounds are fully characterized. Single crystalline X-ray diffraction (XRD) studies on the two compounds reveal layered packings and structural disorders in the lattice. Electrochemical impedance spectroscopy (EIS) measurements indicate high Li+ ionic conductivity (> 10-6 S/cm) of LEMC. Remarkable difference is observed regarding the chemical compositions and formation routes of the SEIs on the identical sulfur cathodes in Li-S vs. Na-S batteries. The formation of SEIs is found closely associated with fundamental issues such as ion solvation structures, cation coordination, etc. Operando studies on solid-liquid interface in an electrochemical cell carried out by ambient-pressure X-ray photoelectron spectroscopy (AP-XPS) visualize ionic structures in an electrical double layer (EDL) in a Au/sulfide aqueous system. We observe monolayer adsorption of bisulfide (HS-) on Au and spatial distributions of HS- in liquid/gas interface.