Ceramic solid electrolytes conducting primarily a specific ion but with minuscule electron leakage are used in many electrochemical devices. Their degradation phenomena may be classified into two broad categories─a slow transverse mode accumulating damage normal to the ionic current direction and a fast longitudinal mode accumulating degradation parallel to the current direction. Examples of the transverse mode include oxygen bubbles on transverse grain boundaries, in-plane electrolyte cracking in solid oxide electrolysis cells, and cathodic reduction of beta-alumina electrolytes in Na–S batteries. Examples of the longitudinal mode include short-circuiting dendrite formation in metal batteries of both the Na–S type and the all-solid-state lithium metal type. Analogous instability modes are also seen in field-assisted ceramic processing, dielectric devices, and memristors. These phenomenological similarities across different devices, operating conditions, and technologies, as well as the origins of their damage mechanisms, can be understood in terms of the highly nonlinear spatial distributions of the minority carriers (electron/hole) and the chemical potential of the equivalent charge-neutral species such as O2; such distributions can in turn cause or exacerbate damaging concentrations of stress and electric fields. This review also outlines strategies for improving material designs to mitigate degradation, which will be especially important for operations and applications under extreme electrochemical conditions.