Fibre Bragg Grating sensors are optical fibre sensors that are now widely used in civil, mechanical and aerospace engineering for structural health monitoring and damage detection purposes. Typical parameters to be measured are strain and temperature, but also rotation, pressure, vibrations, the distance between stationary and moving or rotating components and concentration of chemical substances can be registered. These sensors have numerous advantages with respect to their piezoelectric counterparts, such as light weight, small dimensions, immunity to electromagnetic interference caused by nearby electronic devices. One of the most notable advantages of Fibre Bragg Grating sensors is the multiplexing capability, meaning that several tens to hundreds of sensors can be stacked together to increase the number of measurement points. This is a key advantage in structural health monitoring and damage detection in aerospace, pavement, bridge and other structures, where numerous points on the structure are subjected to high stresses. Moreover, fibre optical sensors are fully passive - they are capable of functioning without power supply. This review paper deals with highlighting the usage of Fibre Bragg Grating sensors in structural health monitoring and damage detection in various types of structures, namely, civil structures (bridges, pavements) and lightweight structures (aircraft, thin-walled composites), thus underlining a great significance of these sensors in structural safety.