Solid-state electrolytes (SEs) as an effective alternative for conventional liquid electrolytes can achieve much higher energy density, safety, and overcome most issues of Li-ion batteries (LIBs). Additional attractive features of the Solid-State Batteries (SSBs) that employ SEs include high thermal stability at elevated temperatures, a wide electrochemical window, high ionic conductivity, lower capacity fading, and a better suppression of internal short circuit. There are challenges/issues that need further research to enhance the SSBs before adopting them to large-scale applications. These include mechanical and chemical stability, ionic transport, interfacial resistance, stress, cracking, wetting behavior, and Li dendrite growth. In this review, we present a detailed account of the current state of SSB research, describe the challenges associated with these batteries, outline the potential solutions, and highlight the future research directions. Finally, we also present a case for the multi-scale computational techniques using a combination of quantum mechanics, molecular dynamics and macro-scale mathematical modeling techniques as a feasible approach to study these research questions.