Composite materials are widely used in most industries due to their high specific strength, specific stiffness, and their relatively lighter weight compared to other traditional materials. However, the presence of defects arising from manufacturing processes or during service loads can make these structures more susceptible to a diminished performance. Furthermore, the former defects are inevitable in composite structures, but they can be reduced. Each type of defect requires specific inspection techniques and configurations. In this work, a review of the different types of composites manufacturing processes and their corresponding resultant defects is presented with the various nondestructive evaluation techniques employed for these defects’ characterization. The emphasis of this paper is on ultrasonic inspection and detection techniques for they present high sensitivity to surface/subsurface discontinuities, superior depth of ultrasonic penetration for flaw detection, feasibility on large scales, and instantaneous and detailed images production. Notably, noncontact ultrasonic testing techniques are also reviewed, air-coupled techniques in specific, and highlighted as a fine alternative to conventional contact inspection systems as they reduce the restrictions that coexist with the use of couplants. Moreover, these ultrasonic testing techniques are summarized to show the latest research progress achieved in the field of air-coupled ultrasonic inspection systems for manufacturing defects’ monitoring in composite structures including delamination, porosity, dryness, waviness, and resin lack/excess. Finally, we highlight the type and central frequency of the transducers and experimental results present in literature and obtained in terms of both detection and size of the defects.