Fibre-reinforced polymer (FRP) composite materials are widely used in different branches of industry, especially in aerospace, owing to their low mass, high strength and stiffness, and good fatigue and corrosion resistance. However, these materials are prone to the impact damage. Especially dangerous are barely visible impact faults, since it is difficult to detect them. If left unrepaired, they can lead to collapse of the whole structure. Hence, a continuous monitoring for loads and possible impact faults in these structures is crucial. Traditionally, this is realized via surface-mounted sensor technologies. However, smart structures with internally embedded sensors offer several advantages — sensor protection from the environment, better coupling to the structure, and no disruption of surface geometry, which is essential for aerodynamic elements, also allowing monitoring in the real time without stopping their operations. The most popular existing smart structural solutions — piezoelectric sensor networks and fibre optics, are reviewed along with other, less common sensor choices. This review also covers the limitations associated with sensor embedment, whose addressing would bring the society to a more reliable, cheaper, and efficient maintenance of transportation and infrastructure.