Current Li battery technology employs graphite anode and flammable organic liquid electrolytes. Thus, current Li battery is always facing the problems of low energy density and safety. Additionally, sustainable supply of Li due to scarce abundance of Li sources is another problem. All-solid-state Mg battery is expected to solve the problems owing to non-flammable solid-state electrolytes, high capacity/safety of divalent Mg metal anode and high abundance of Mg sources. Therefore, solid-state electrolytes and all-solid-state Mg battery have been researched intensively last two decades. However, realization of all-solid-state Mg battery is still far. In this article, we review recent research progress on all-solid-state Mg battery so that researchers can pursue recent research trend of all-solid-state Mg battery. At first, solid-state electrolyte research is described briefly in the categories of inorganic, organic and inorganic/organic composite electrolytes. After that, the recent research progress of all-solid-state Mg battery is summarized and analyzed. To help readers, we tabulate electrode materials, experimental conditions and performances of all-solid-state Mg battery so that the readers can find necessary information at a glance. In the last, challenges to realize the all-solid-state Mg batteries are visited.