Continuous fibre-reinforced thermoplastics (FRTPs) are replacing metals in certain applications in the aerospace industry due to their superior properties e.g., high strength-to-weight ratio and good fatigue resistance. Adopting these lightweight materials in vehicles is a solution for improving vehicle efficiency across the transport industry. Among various manufacturing techniques for FRTP parts, stamp forming is one of the most advantageous when small structures and mass production are targeted. However, a significant barrier for this technique is the quality control of manufacturing. The current paper reviews the development of stamp forming technology, benefits of using such technology and the typical quality issues in stamp forming of FRTP parts. First, advantages of stamp forming, compared to other thermoforming techniques, are discussed, followed by a review of the historical development of the process. Second, deformation mechanisms of FRTPs during stamp forming are examined, with particular focuses on the frictional behaviour and testing thereof. Third, the main defects associated with stamp forming are considered, alongside suggestions towards reducing their presence. Finally, an extensive survey of the effect of process parameters on the mechanical properties of formed parts is included, with generally expected trends highlighted and methodologies for finding optimum conditions presented. Based on the thorough review of state-of-the-art stamp forming, future trends and research gaps to be tackled for widening the applicability of FRTP stamp forming are suggested.