The food industry faces many challenges, including the need to feed a growing population, food loss and waste, and inefficient production systems. To cope with those challenges, digital twins that create a digital representation of physical entities by integrating real-time and real-world data seem to be a promising approach. This paper aims to provide an overview of digital twin applications in the food industry and analyze their challenges and potentials. Therefore, a literature review is executed to examine digital twin applications in the food supply chain. The applications found are classified according to a taxonomy and key elements to implement digital twins are identified. Further, the challenges and potentials of digital twin applications in the food industry are discussed. The survey revealed that the application of digital twins mainly targets the production (agriculture) or the food processing stage. Nearly all applications are used for monitoring and many for prediction. However, only a small amount focuses on the integration in systems for autonomous control or providing recommendations to humans. The main challenges of implementing digital twins are combining multidisciplinary knowledge and providing enough data. Nevertheless, digital twins provide huge potentials, e.g., in determining food quality, traceability, or designing personalized foods.