Sustainable production of healthy food for a growing global population, in the face of the uncertainties of climate change, represents a major challenge for the coming decade. Livestock provide food with high nutritional value but are frequently fed on human-edible crops and are associated with significant production of greenhouse gases. Recent years have seen increasing interest in the farming of insects as a sustainable source of human food, or as a replacement of ingredients such as soya or fishmeal in the feeds of terrestrial livestock or fish. This review provides an overview of insect physiology and growth regulation, considers the requirements for insect farming and mass production, and summarizes the nutritional value of the 10 most commonly studied insect species, before reviewing the literature on the use of insects as feed and food. We highlight the challenges required to develop a sustainable, safe, and affordable insect farming industry.