Superior stability and safety are key promises attributed to all-solid-state batteries (ASSBs) containing solid-state electrolyte (SSE) in comparison to their conventional counterparts utilizing liquid electrolyte. To unfold the full potential of ASSBs, SSE materials are desirable that are stable in contact with both the low and the high potential electrode. The electrochemical stability window is conveniently used to assess the SSE--electrode interface stability. In the present work, we review the most important methods to compute the SSE stability window. We find that the stoichiometry stability method represents a bridge between HOMO--LUMO method and phase stability method (grand canonical phase diagram). We further provide implementations of these methods for SSE material screening and we compare their results for the relevant Li- and Na-SSE materials LGPS, LIPON, LLZO, LLTO, LATP, LISICON, and NASICON.