The safety of food contact materials is a hot topic since chemicals can migrate from packaging into food, thus raising health concerns about and/or producing changes in the organoleptic properties of foodstuffs. Migration tests are required to demonstrate the compliance with current regulations and to investigate the transferred compounds. In this context, mass spectrometry is the analytical technique of choice for the detection and quantitation of both intentionally added substances, such as antioxidants, stabilizers, processing aids, and non-intentionally added substances (NIAS). Untargeted strategies represent a major analytical challenge, providing a comprehensive fingerprinting of the packaging material and migrating components, allowing for NIAS identification. Hyphenated mass spectrometry-based techniques have been devised for screening the presence of migrating contaminants and for quantitation purposes. Both low-resolution (LRMS) and high-resolution (HRMS) methods were screened, with a special emphasis on the latter because of its capability to directly characterize food contact materials with minimal/no sample preparation, avoiding chromatographic separation, and reducing sample handling, analysis costs, and time. Examples related to the migration of contaminants from existing or newly developed bioplastic materials will be discussed, providing an overview of the most used MS-based methods, covering the state-of-the-art approaches from 2012 up to 2022.