This paper presents and discusses attributes of polymer-ceramic (PEO:LiBF4-Li3N and PEO:LiBF4-TiO2) and ceramic-ceramic (Li3N-LiPO3, and Li3N-TiO2) composite electrolytes. The polymer-ceramic type of electrolytes have been investigated by some researchers around the world and they provide certain advantages over the polymer electrolytes. This work specifically covers the effect of annealing on the conductivity of the aforementioned electrolytes. Although the history of ceramic-ceramic composite electrolyte is older than that of polymer-ceramic electrolytes, it has received very little attention in recent years. This paper presents some promising avenues and preliminary electrochemical data on ceramic-ceramic composite electrolytes.