Clean and highly efficient production of solar fuels as well as effective methods to store solar fuels have long been sought to solve global energy and environmental issues. Among solar fuels such as gaseous hydrogen and carbon monoxide, aqueous hydrogen peroxide (H2O2) is an ideal chemical for energy storage, because endothermic H2O2 decomposition produces only water and oxygen. In addition, H2O2 can be transported in plastic containers with a high energy density. H2O2 can be converted into electricity by using H2O2 fuel cells without a membrane and composed of an anode and a cathode, and they can selectively catalyze H2O2 oxidation or reduction. The one-compartment structure without a membrane is more promising to develop low-costing fuel cells than a two-compartment structure with expensive membranes. This article provides a focused review of recent developments and future perspectives of H2O2 fuel cells without membranes, combined with H2O2 production from seawater and dioxygen in the air by utilizing solar energy.