The massive rise of Big Data generated from smartphones, social media, Internet of Things (IoT), and multimedia, has produced an overwhelming flow of data in either structured or unstructured format. Big Data technologies are being developed and implemented in the food supply chain that gather and analyse these data. Such technologies demand new approaches in data collection, storage, processing and knowledge extraction. In this article, an overview of the recent developments in Big Data applications in food safety are presented. This review shows that the use of Big Data in food safety remains in its infancy but it is influencing the entire food supply chain. Big Data analysis is used to provide predictive insights in several steps in the food supply chain, support supply chain actors in taking real time decisions, and design the monitoring and sampling strategies. Lastly, the main research challenges that require research efforts are introduced.