The key priority in improving the technical and economic performance of gas turbine engines lays in the use of new composite materials. The use of composites in the components of critical load-carrying structures operating under static and dynamic loads during long service lives determines the need to predict the component lives. Also, in order to increase the safety of engine operation and improve the parts manufacturing process, timely defect detection in such structures is of great importance. This article is devoted to the detection of the composite parts defects and damages that occur at different stages of manufacturing and operation. The aim is to investigate the existing methods of non-destructive testing of composite materials, describe their functional concept, and determine the field of their application. The article considers acoustic, thermal, optical, and radiation testing methods. Among the acoustic methods, the phased array method is selected as the most informative and multipurpose. The acoustic emission method is also selected; it will allow real-time monitoring of defect growth during testing. Out of thermal methods, the vibrothermography method was selected as the most advanced among the thermographic sub-methods. It allows using the phenomenon of local defect resonance and thus ensures effective defect detection. Shearography is selected for investigation out of optical methods. The special aspects of the use of X-ray methods are considered through the example of X-ray computed tomography. It is concluded that the approach combining several methods can significantly increase the efficiency of defect detecting and help to assess their criticality. Active thermal testing is well suited for fast scanning of large-sized parts and searching for areas of defect accumulation. In the following, local methods, such as impedance, vibrothermography, or one of the ultrasonic, should be used. To measure deformations under static load, it is a good practice to use shearography. To identify progressive defects under static load, it makes sense to use the acoustic emission method.