Complex hydrides exhibit various energy-related functions such as hydrogen storage, microwave absorption, and neutron shielding. Furthermore, another novel energy-related function was recently reported by the authors; lithium fast-ionic conduction, which suggests that complex hydrides may be a potential candidate for solid electrolytes in lithium-ion batteries. This review presents the recent progress in the development of lithium fast-ionic conductors of complex hydrides. First, the fast-ionic conduction in LiBH4 as a result of clarifying the mechanism of microwave absorption is presented, and then the conceptual development of complex hydrides as a new type of solid-state lithium fast-ionic conductors in LiBH4–, LiNH2–, and LiAlH4-based complex hydrides is discussed. Finally, the future prospects of this study from both application and fundamental viewpoints are described: possible use as solid electrolytes for batteries, formation of ionic liquids in complex hydrides, and similarity between complex hydrides and Laves-phase metal hydrides.