As battery technologies are in continuous development, and especially due to the rapid growth in vehicle electrification, which requires large (e.g., 100 s of kg) battery packs, there has been a growing demand for more efficient, reliable, and environmentally friendly materials. Solid-state post-lithium-ion batteries are considered a possible next-generation energy storage technology. One immediate advantage of these power sources over commercial lithium-ion batteries is the potential of solving the resource issues facing LIBs, especially as cost-effective alternatives. The second advantage is the removal of flammable liquid electrolytes. The solid electrolytes are more resistant to changes in temperature and physical damage, produce up to 80% less heat, and are able to handle more charge/discharge cycles before degradation makes them unusable. All these features point towards a longer battery life. Other immediate gains include the removal of the membrane and casing required for a liquid electrolyte. This may reduce the weight and volume of each cell, leading to an increase in the energy density of the battery. In this review, we describe recent achievements in the development of sodium, potassium, and magnesium solid-state batteries. It can be revealed that while the research community has progressed greatly towards solid-state alkali and alkaline-earth batteries, much more improvement in the room temperature ionic conductivity of solid electrolytes is required. For the practical applications of these systems, the stability and interfacial reactions of solid electrolytes should be explored in great depth.