Thermoplastic composites have the characteristics of high strength, fatigue resistance and easy recycling. They have received wide attention and are used in construction, automobile and other fields. An accurate monitoring technique is necessary for monitoring their internal state in the molding process and structure health in the service process. Traditional mechanical and electrical sensors have many disadvantages, such as large size and slow response. Therefore, they are not appropriate for embedded measuring and real-time monitoring. Optical fiber Bragg grating (FBG) sensors present many advantages over traditional and other advanced sensors, such as resistance to electromagnetic interference, light weight and less influence on materials. Generally, FBGs are embedded in composites and/or structures to monitor temperature and strain. The principle of FBG sensor and three key demodulation techniques are introduced firstly, including tunable Fabry-Perot (F-P) filter demodulation, especially the high-speed demodulation technique based on swept wavelength tunable laser, linear filter demodulation and matched grating. Secondly, the progress of monitoring technology based on FBGs for three molding scheme is reviewed, including hot compression molding, fused deposition molding and automated fiber placement molding. Thirdly, the progress of structural health monitoring for thermoplastic composites is also reviewed. Finally, some intelligent thermoplastic composite structures based on FBGs are introduced.