Safe, healthy, and resilient food supply chains are essential to ensuring the livelihood and well-being of humans and societies, as well as local and global economies. However, the ability to provide and sustain access to nutritious and safe food continues to be a major concern and a challenge for almost any country around the world, including developed countries. Some serious and global public health risks arise from food supply chains. These include food safety and adulteration risks in which unsafe food is sold for human consumption, antimicrobial resistance risks that are becoming increasingly prevalent due to the overuse of antibiotics, zoonotic disease risks (i.e., viruses and diseases that transfer from animals to humans through food supply chains), food waste, and also food security issues such as food deserts and the diet disparity among different segments of the population. This article gives an introduction to these various risks and reviews directions in the current academic literature to address these challenges. The article also seeks to highlight important new research directions in these areas, and especially those that might be of significant interest to the operations research community.