Despite the large debate about the relationship between ultra-processed foods and the prevalence of some diet-related diseases, the innovative potential of various processing technologies has been evidenced in pathways that could lead to modifications of the food matrix with beneficial health effects. Many efforts have been directed toward the conjugation of a healthy diet and sustainable exploitation of natural resources for the preparation of accessible foods. This minireview highlights the possible links between processing, sustainability, and circular economy through the valorization of by-products that could be exploited to prepare nutrient-rich ingredients at lower economic and environmental costs. The assessment of the quality and safety of functional foods based on ingredients derived from food waste requires a more robust validation by means of the food-omics approach, which considers not only the composition of the final products but also the structural characterization of the matrix, as the bioaccessibility and the bioavailability of nutrients are strictly dependent on the functional characteristics of the innovative ingredients.