All solid-state lithium-ion batteries have gained great interest due to their potential for high energy density and safety. It is a general belief that solid electrolytes, in view of their high stiffness, should resist Li dendrite formation, allowing all solid-state batteries to be equipped with lithium metal anodes. Nevertheless, experiments have shown that distinctive mechanisms of dendrite propagation develop in ceramic electrolytes, too. Li dendrites thus remain an open challenge even in solid electrolytes since they critically reduce the performance of all solid-state batteries and eventually lead to short circuits. A clear understanding of the mechanisms that trigger and propagate Li dendrites is of outmost relevance to their suppression. Theoretical modeling can elucidate the fundamental principles and influence factors in Li dendrite nucleation, growth, and penetration in solid electrolytes. A literature review on modeling and simulations of such detrimental processes is provided in this paper.
