The European Union (EU) is committed to transitioning toward a circular economy model, with food waste being one of the areas to be targeted. To close the loop of food waste generated during food processing and discarded at the retail or consumption phases, research and innovation parties proposed to valorize agro-food by-products to produce novel foods and food improvement agents (food additives, food enzymes, and food flavorings). In the EU, the authorization of such novel foods and food improvement agents is governed by different regulatory frameworks. A centralized safety assessment by the European Food Safety Authority (EFSA) is the prerequisite for their authorization through the so-called Union Lists. Up to December 2023, EFSA published 45 scientific opinions on the safety of novel foods, food enzymes, and food additives derived from by-products of plant and animal origin. The current study illustrates examples of these by-products for the production of novel foods or food improvement agents and the data requirements behind their respective safety assessments conducted by EFSA. In this review, applications on novel foods, food enzymes, and food additives received by EFSA were screened and analyzed to find the common scientific requirements and differences in terms of the safety evaluation of such products. Various by-products (i.e., corncobs, coffee husks, spent grains of barley and rice, grape pomace, pumpkin peels, bovine whey, eggshells, shrimp heads, and animal organs or tissues) were described in the applications as being processed (extraction, physical treatments, and chemical and enzymatic reactions) to obtain novel foods and food improvement agents. The heterogeneity and complexity of these products emphasize the challenge of their safety assessment, depending on the characteristics of each product. However, as this study shows, the scientific requirements underpinning their safety do not differ substantially in the different regulated product areas considered, with similar information needed to assess their safety in terms of identity, production process, compositional characterization, proposed/intended uses and exposure assessment, toxicological information, and allergenicity data. Additional nutritional information and data on the history of use are required in the case of novel foods.