Structural power composites stand out as a possible solution to the demands of the modern transportation system of more efficient and eco-friendly vehicles. Recent studies demonstrated the possibility to realize these components endowing high-performance composites with electrochemical properties. The aim of this paper is to present a systematic review of the recent developments on this more and more sensitive topic. Two main technologies will be covered here: (1) the integration of commercially available lithium-ion batteries in composite structures, and (2) the fabrication of carbon fiber-based multifunctional materials. The latter will be deeply analyzed, describing how the fibers and the polymeric matrices can be synergistically combined with ionic salts and cathodic materials to manufacture monolithic structural batteries. The main challenges faced by these emerging research fields are also addressed. Among them, the maximum allowable curing cycle for the embedded configuration and the realization that highly conductive structural electrolytes for the monolithic solution are noteworthy. This work also shows an overview of the multiphysics material models developed for these studies and provides a clue for a possible alternative configuration based on solid-state electrolytes.