Solid-state NMR spectroscopy is an established experimental technique which is used for the characterization of structural and dynamic properties of materials in their native state. Many types of solid-state NMR experiments have been used to characterize both lithium-based and sodium-based solid polymer and polymer–ceramic hybrid electrolyte materials. This review describes several solid-state NMR experiments that are commonly employed in the analysis of these systems: pulse field gradient NMR, electrophoretic NMR, variable temperature T1 relaxation, T2 relaxation and linewidth analysis, exchange spectroscopy, cross polarization, Rotational Echo Double Resonance, and isotope enrichment. In this review, each technique is introduced with a short description of the pulse sequence, and examples of experiments that have been performed in real solid-state polymer and/or hybrid electrolyte systems are provided. The results and conclusions of these experiments are discussed to inform readers of the strengths and weaknesses of each technique when applied to polymer and hybrid electrolyte systems. It is anticipated that this review may be used to aid in the selection of solid-state NMR experiments for the analysis of these systems.