Solid electrolytes (SEs) have garnered increased attention for their promise to enable higher volumetric energy density and enhanced safety required for future battery systems. SEs are not only a key constituent in all-solid-state batteries, but also are important "protectors" of Li-metal anodes in next-generation battery configurations, such as Li-air, Li-S, redox flow batteries, among others. The impedance at interfaces associated with SEs, e.g. internal grain/phase boundaries and their interfacial stability with electrodes, represent two key factors limiting the performance of SEs, yet analyzing these interfaces experimentally at the nano/atomic scale is generally challenging. A mechanistic understanding of the possible instability at interfaces and propagation of interfacial resistance will pave the way to the design of high-performance SE-based batteries. In this review, we briefly introduce the fundamentals of SEs and challenges associated with their interfaces. Next, we discuss experimental techniques that allow for atomic-to-microscale understanding of ion transport and stability in SEs and at their interfaces, specifically highlighting the applications of state-of-art and emerging ex situ and in situ transmission electron microscopy (TEM) and scanning TEM (STEM). Representative examples from current literature that exemplify recent fundamental insights gained from these S/TEM techniques are highlighted. Applicable strategies to improve ion conduction and interfaces in SE-based batteries are also discussed. This review concludes by highlighting opportunities for future research that will significantly promote the fundamental understanding of SEs, specifically further developments in S/TEM techniques that will bring new insights into the design of high-performance interfaces for future electrical energy storage.