Food businesses in the European Union are preparing for a carbon-neutral future by gradually transitioning to a circular way of operating. Building upon results from the EU REFRESH project, we consider the most valuable food processing by-streams in Europe and discuss potential food safety risks that must be considered while valorizing them for human consumption. These risks are weighed against the nutritional benefits offered by these products and their potential applications in food supply chains. Broadly, we examine whether it is possible for spent grains, cheese whey, fruit and vegetable scraps, meat processing waste, and oilseed cakes and meals to be safe, sustainable, and nutritionally valuable at the same time. The discussion highlights that valorizing by-products obtained from food processing operations is feasible on a large scale only if consumers deem it to be a safe and acceptable practice. Extracting valuable compounds from by-products and using them in the preparation of functional foods could be a way to gain consumer acceptance. Furthermore, we find that current EU food safety legislation does not sufficiently accommodate food processing by-products. A way to bridge this regulatory gap could be through the adoption of private food safety standards that have shown proclivity for sustainability-related issues in food supply chains. Finally, by proposing a decision tree, we show that it is indeed feasible for some food processing by-products to be valorized while ensuring sustainability, food safety, and nutritional relevance.