Organic electrochemical transistors (OECTs) continue to be the subject of much detailed and systematic study, being suitable for a diverse range of applications including bioelectronics, sensors, and neuromorphic computing. OECTs conventionally use a liquid electrolyte, and this architecture is well suited for sensing or bio-interfacing applications where biofluids or liquid samples can be used directly as the electrolyte. A more recent trend is solid-state OECTs, where a solid or semi-solid electrolyte such as an ion gel, hydrogel or polyelectrolyte replaces the liquid component for an all-solid-state device. The growing interest in solid-state OECTs has been motivated by the many applications where high density and individually addressable OECTs are desirable and necessary, such as logic circuits and neuromorphic computing. Therefore, solid-state OECTs are being increasingly explored for easily integrable and compact systems. In this review, we discuss solid-state OECTs with the purpose of introducing readers to the breadth of tested and feasible solid electrolytes and guide them through key materials and device design considerations. We highlight applications, key challenges to be overcome and opportunities for future research and development.