Background: Food contact materials (FCM) may contain non-intentionally added substances (NIAS) as a result of reaction by-products, oligomers, degradation processes, chemical reactions between packaging materials and foodstuff, or as impurities from the raw materials used for their production. Scope and approach: In this review, current approaches for the detection and identification of NIAS from paper and board FCM are presented. Reviewed are the definition of NIAS, approaches for NIAS identification and quantification, the comprehensive analysis of NIAS and the role of in silico tools and bioassays. Key Findings and Conclusions: NIAS in paper and board are mostly components from printing inks, adhesives, sizing agents and surface coatings. Recycled paper contains overall more NIAS than fresh paper. Targeted analysis is generally performed for predicted NIAS, whereas an untargeted, or full-scan screening method is applied to detect and identify unpredicted NIAS. Sample preparation and contact conditions fall in two categories; migration and extraction. Migration studies are performed with food simulants while extraction studies are Soxhlet or ultrasound assisted solvent extraction. In untargeted analysis in silico tools are gaining importance in the identification of NIAS. Bioassays are used to determine the bioactivity of extracts or fractions in order to assess the potential toxicity of NIAS present in the mixture. A combination of bioassays and chemical analysis is used to direct the identification of unknown bioactive NIAS in complex mixtures like those from paper and board FCM. However, future research is required into the selection of bioassays since these should not only be sensitive enough for detecting all compounds of concern but should also have a relevance with human health.