Radical innovations for all aircraft systems and subsystems are needed for realizing future carbon-neutral aircraft, with hybrid-electric aircraft due to be delivered after 2035, initially in the regional aircraft segment of the industry. Electrical energy storage is one key element here, demanding safe, energy-dense, lightweight technologies. Combining load-bearing with energy storage capabilities to create multifunctional structural batteries is a promising way to minimize the detrimental impact of battery weight on the aircraft. However, despite the various concepts developed in recent years, their viability has been demonstrated mostly at the material or coupon level, leaving many open questions concerning their applicability to structural elements of a relevant size for implementation into the airframe. This review aims at providing an overview of recent approaches for structural batteries, assessing their multifunctional performance, and identifying gaps in technology development toward their introduction for commercial aeronautic applications. The main areas where substantial progress needs to be achieved are materials, for better energy storage capabilities; structural integration and aircraft design, for optimizing the mechanical-electrical performance and lifetime; aeronautically compatible manufacturing techniques; and the testing and monitoring of multifunctional structures. Finally, structural batteries will introduce novel aspects to the certification framework.