Design and fabrication of electrochemical energy storage systems with both high energy and power densities as well as long cycling life is of great importance. As one of these systems, Battery-supercapacitor hybrid device (BSH) is typically constructed with a high-capacity battery-type electrode and a high-rate capacitive electrode, which has attracted enormous attention due to its potential applications in future electric vehicles, smart electric grids, and even miniaturized electronic/optoelectronic devices, etc. With proper design, BSH will provide unique advantages such as high performance, cheapness, safety, and environmental friendliness. This review first addresses the fundamental scientific principle, structure, and possible classification of BSHs, and then reviews the recent advances on various existing and emerging BSHs such as Li-/Na-ion BSHs, acidic/alkaline BSHs, BSH with redox electrolytes, and BSH with pseudocapacitive electrode, with the focus on materials and electrochemical performances. Furthermore, recent progresses in BSH devices with specific functionalities of flexibility and transparency, etc. will be highlighted. Finally, the future developing trends and directions as well as the challenges will also be discussed; especially, two conceptual BSHs with aqueous high voltage window and integrated 3D electrode/electrolyte architecture will be proposed.