Additive manufacturing (AM) enables the production of parts with extremely complex shapes, such as lattice structures and internal structures (cavities, channels). As a result of this geometric complexity, the applicability of most conventional nondestructive testing (NDT) techniques to AM parts is limited, and innovative volumetric NDT methods are needed for quality control. Few established volumetric NDT methods are suitable for inspecting the integrity of parts with complex geometries. X-ray computed tomography (XCT) is widely recognized as the most powerful method for detecting and evaluating the dimensions of structural flaws and also for checking the compliance of parts with their numerical model. However, it is an expensive method. The image analysis takes more time than is appropriate for routine inspection, and the files are large and, thus, difficult to handle. Furthermore, XCT is not suitable for large and high-density parts. Alternative methods are therefore needed. Investigation of resonant acoustic methods such as resonant ultrasound spectroscopy (RUS) or electromagnetic-acoustic resonance methods, linear or nonlinear, has shown great potential. RUS methods are global, enabling identification of defective parts based on analysis of their natural resonant frequencies. There are several variants of RUS methods, but their basic principles are similar. They can inspect any part shape, and they are insensitive to inherent surface roughness. In addition, although they are global volumetric methods (“pass/fail”), they can inspect parts of any size, unlike XCT, which can determine the locations of defects but is restricted by the size or density of the parts. Moreover, compared to XCT, they are simple to implement, easy to use, quite affordable, and the inspection of the parts is particularly fast, which is very suitable for routine inspection. This article describes the capabilities of various linear RUS methods, as well as a nonlinear electromagnetic-acoustic resonance method for quality assurance of AM parts.