In this review, we present current approaches in the analysis of food-packaging contaminants. Gas and liquid chromatography coupled to mass spectrometry detection have been widely used in the analysis of some relevant families of these compounds such as primary aromatic amines, bisphenol A, bisphenol A diglycidyl ether and related compounds, UV-ink photoinitiators, perfluorinated compounds, phthalates and non-intentionally added substances. Main applications for sample treatment and different types of food-contact material migration studies have been also discussed. Pressurized Liquid Extraction, Solid-Phase Microextraction, Focused Ultrasound Solid-Liquid Extraction and Quechers have been mainly used in the extraction of food contact material (FCM) contaminants, due to the trend of minimising solvent consumption, automatization of sample preparation and integration of extraction and clean-up steps. Recent advances in analytical methodologies have allowed unequivocal identification and confirmation of these contaminants using Liquid Chromatography coupled to High Resolution Mass Spectrometry (LC-HRMS) through mass accuracy and isotopic pattern applying. LC-HRMS has been used in the target analysis of primary aromatic amines in different plastic materials, but few studies have been carried out applying this technique in post-target and non-target analysis of FCM contaminants.