This paper sets out to review the current state of the art in applying self-healing/self-repair to high-performing advanced fiber-reinforced polymer composite materials (FRPs). A significant proportion of self-healing studies have focused so far on developing and assessing healing efficiency of bulk polymer systems, applied to particulate composites or low-volume fraction fiber-reinforced materials. Only limited research is undertaken on self-healing in advanced structural FRP composite materials. This review focuses on what is achieved to date, the ongoing challenges which have arisen in implementing self-healing into FRPs, how considerations for industrialization and large-scale manufacture must be considered from the outset, where self-healing may provide most benefits, and how a functionality like self-healing can be validated for application in real structures. Systems are compared in terms of process parameters, resulting mechanical properties, methods of healing assessment, as well as values of healing quantification. Guidelines are further given for a concerted effort to drive toward standardization of tests and the use of specific reinforcement architectures in order to allow reliable comparison between the available healing systems in structural composites.