Due to the increasing occurrence of disruptive events caused by both human and also natural disasters, supply chain risk management has become an emerging research field in recent years, aiming to protect supply chains from various disruptions and deliver sustainable and long-term benefits to stakeholders across the value chain. Implementing optimum designed risk-oriented supply chain management can provide a privileged position for various businesses to extend their global reach. In addition, using a proactive supply chain risk management system, enterprises can predict their potential risk factors in their supply chains, and achieve the best early warning time, which leads to higher firms’ performance. However, relatively little is known about sustainable risks in food supply chains. In order to manage the ever-growing challenges of food supply chains effectively, a deeper insight regarding the complex food systems is required. Supply chain risk management embraces broad strategies to address, identify, evaluate, monitor, and control unpredictable risks or events with direct and indirect effect, mostly negative, on food supply chain processes. To fill this gap, in this paper we have critically discussed the related supply chain risk management literature. Finally, we propose a number of significant directions for future research.