Paper and board are widely used as food contact materials. For such sensitive applications, consumer safety regarding the transfer of chemical components and contaminants to the food needs to be established. Such safety assessments are becoming increasingly challenging not only due to intentionally added substances but also non-intentionally added substances. In the European Union, compliance testing and safety evaluation of paper in food contact are largely based on national legislation and standards. The underlying tests are conventional methods, often overestimating and sometimes underestimating the migration into food. In this article, the relevant standard test methods are contrasted with currently available scientific knowledge. The scientific approaches to develop and identify suitable test methods are critically reviewed. Furthermore, theoretical predictions via mathematical modeling, with the aim to realistically simulate transfer to food, are presented and discussed in comparison with available migration studies with foods. Objectives are to (i) summarize the actual scientific knowledge in the field and draw conclusions regarding the potential and limitations of the existing test methods and (ii) identify research gaps toward a better qualitative and quantitative understanding of transport processes of volatile and non-volatile substances from paper and board into foods.