Several food contact materials (FCMs) contain non-intentionally added substances (NIAS), and most of the substances that migrate from plastic food packaging are unknown. This review aimed to situate the main challenges involving unknown NIAS in plastic food packaging in terms of identification, migration tests, prediction, sample preparation, determination methods and risk assessment trials. Most studies have identified NIAS in plastic materials as polyurethane adhesives (PU), polyethylene terephthalate (PET), polyester coatings, polypropylene materials (PP), multilayers materials, plastic films, polyvinyl chloride (PVC), recycled materials, high-density polyethylene (HDPE) and low-density polyethylene (LDPE). Degradation products are almost the primary source of NIAS in plastic FCMs, most from antioxidants as Irganox 1010 and Irgafos 168, following by oligomers and side reaction products. The NIAS assessment in plastics FCMs is usually made by migration tests under worst-case conditions using food simulants. For predicted NIAS, targeted analytical methods are applied using GC-MS based methods for volatile NIAS and GC-MS and LC-MS based methods for semi- and non-volatile NIAS; non-targeted methods to analyze unknown NIAS in plastic FCMs are applied using GC and LC techniques combined with QTOF mass spectrometry (HRMS). In terms of NIAS risk assessment and prioritization, the threshold of toxicological concern (TTC) concept is the most applied tool for risk assessment. Bioassays with sensitive analytical techniques seem to be an efficient method to identify NIAS and their hazard to human exposure; the combination of genotoxicity testing with analytical chemistry could allow the Cramer class III TTC application to prioritize unknown NIAS. The scientific justification for implementing a molecular weight-based cut-off (<1000 Da) in the risk assessment of FCMs should be reevaluated. Although official guides and opinions are being issued on the subject, the whole chain’s alignment is needed, and more specific legislation on the steps to follow to get along with NIAS.