This paper introduces the concept of structural power composite materials and their possible devices and the rationale for developing them. The paper presents a comprehensive review of the state-of-the-art, highlighting achievements related to structural battery and supercapacitor devices. The research areas addressed in detail for the two types of material devices include: carbon fibre electrodes, structural separators, multifunctional matrix materials, device architectures and material functionalization. Material characterisation, fabrication and validation are also discussed. The paper culminates in a detailed description of scientific challenges, both generic as well as device specific, that call for further research. Particular reference is given to work performed in national and European research projects under the leadership of the authors, who are able to provide a unique insight into this newly emerging and exciting field.