In the last few years, the Internet of Things, and other enabling technologies, have been progressively used for digitizing Food Supply Chains (FSC). These and other digitalization-enabling technologies are generating a massive amount of data with enormous potential to manage supply chains more efficiently and sustainably. Nevertheless, the intricate patterns and complexity embedded in large volumes of data present a challenge for systematic human expert analysis. In such a data-driven context, Computational Intelligence (CI) has achieved significant momentum to analyze, mine, and extract the underlying data information, or solve complex optimization problems, striking a balance between productive efficiency and sustainability of food supply systems. Although some recent studies have sorted the CI literature in this field, they are mainly oriented towards a single family of CI methods (a group of methods that share common characteristics) and review their application in specific FSC stages. As such, there is a gap in identifying and classifying FSC problems from a broader perspective, encompassing the various families of CI methods that can be applied in different stages (from production to retailing) and identifying the problems that arise in these stages from a CI perspective. This paper presents a new and comprehensive taxonomy of FSC problems (associated with agriculture, fish farming, and livestock) from a CI approach; that is, it defines FSC problems (from production to retail) and categorizes them based on how they can be modeled from a CI point of view. Furthermore, we review the CI approaches that are more commonly used in each stage of the FSC and in their corresponding categories of problems. We also introduce a set of guidelines to help FSC researchers and practitioners to decide on suitable families of methods when addressing any particular problems they might encounter. Finally, based on the proposed taxonomy, we identify and discuss challenges and research opportunities that the community should explore to enhance the contributions that CI can bring to the digitization of the FSC.