All-solid-state (ASS) lithium-ion battery has attracted great attention due to its high safety and increased energy density. One of key components in the ASS battery (ASSB) is solid electrolyte that determines performance of the ASSB. Many types of solid electrolytes have been investigated in great detail in the past years, including NASICON-type, garnet-type, perovskite-type, LISICON-type, LiPON-type, Li3N-type, sulfide-type, argyrodite-type, anti-perovskite-type and many more. This paper aims to provide comprehensive reviews on some typical types of key solid electrolytes and some ASSBs, and on gaps that should be resolved.