Faced with the challenges associated with sustainably feeding the world’s growing population, the food industry is increasingly relying on operations research (OR) techniques to achieve economic, environmental and social sustainability. It is therefore important to understand the context-specific model-oriented applications of OR techniques in the sustainable food supply chain (SFSC) domain. While existing food supply chain reviews provide an excellent basis for this process, the explicit consideration of sustainability from a model-oriented perspective along with a structured outline of relevant SFSC research techniques are missing in extant literature. We attempt to fill this gap by reviewing 83 related scientific journal publications that utilise mathematical modelling techniques to address issues in SFSC. To this end, we first identify the salient dimensions that include economic, environmental and social issues in SFSC. We then review the models and methods that use these dimensions to solve issues that arise in SFSC. We identify some of the main challenges in analytical modelling of SFSC as well as future research directions.