There has been great interest in developing solid electrolytes (SEs) and all-solid-state batteries (ASSBs) with the aim of enabling highly safe and durable batteries that also might be a key technology to the success of future electronics and electric vehicles (EVs). However, the development of SEs and ASSBs tends to be plagued by limitations that originate from problematic contact issues occurring at numerous solid-solid interfaces. Therefore, we believe that deep understanding of the current issues and advanced technologies to address them is important and may be vital to progress regarding practical applications of ASSBs. In the present review, we first classify various types of SEs into a few groups and summarized their characteristics to help understand the current status of SEs and ASSBs. Then, we discuss the types of interfaces and relevant issues, which are comprehensively arranged and reviewed according to the interface type based on where they make contact; we also highlight advanced technologies that present potential solutions for the current challenges associated with SEs and ASSBs. This review aims to help researchers achieve current knowledge of ASSBs and understand the direction of future research trends.