Fibre-reinforced composite materials are extensively used for manufacturing critical engineering components in diverse applications, which demands intelligent and reliable structural health monitoring (SHM) schemes to prevent catastrophic failures associated with composite structures. Composite materials have complex failure mechanisms, and it is essential to employ reliable SHM methods with high accuracy to detect damages at the incipient stage. Although there are several SHM technologies available, no single strategy is impeccable for tackling all damage types due to the incredibly complex failure mechanisms of the composite materials. Machine learning (ML) methods are frequently integrated to compensate for the limitations of the traditional SHM methods. This paper presents the state-of-the-art sensory methods and deep learning (DL) techniques while emphasizing the future directions for the engineering and scientific community interested in developing novel SHM systems for fibre-reinforced polymer composite structures intended for civil, aerospace, automotive, marine, oil and gas exploration industries.