Food spoilage is a natural process that influences the quality and safety of food products, negatively affecting their nutritional and organoleptic composition. In these regards, traditional industrial food preservation processes often rely on the use of traditional preservation techniques to extend food shelf life, while ensuring microbiological and chemical stability without compromising the product’s sensory characteristics. However, in recent years, consumers have become increasingly wary of chemical food additives; they often associate their use with potential health risks and negative impact on product appeal. In addition, this is compounded by an increasingly compellent European regulatory framework, as well as efforts in the search of natural and sustainable alternatives for food preservation. In this context, this review explores the potential of natural additives, such as polyphenols, flavonoids, and antioxidants, derived from agro-industrial waste, including fruit peels, vegetable by-products, and seeds. These compounds exhibit strong antioxidant and antimicrobial properties, which not only extend the shelf life of food products but also enhance their safety and quality. Considering vegetable wastes (i.e., pomegranate peels, olive leaves, olive mill wastewater, and grape pomace) as the main by-products from which natural additives can be extracted, this study provides an overview of their efficacy in preventing lipid oxidation and reducing microbial growth, while maintaining sensory properties. This could represent an opportunity both for maintaining food quality and prolonging food shelf life by valorizing by-products to be otherwise disposed of, and also contribute to mitigating the environmental impact associated with the food industry and to optimize food preservation processes. In addition, it highlights the possibility of employing sustainable alternatives to synthetic additives, capable of extending the shelf life of food products while ensuring their safety for human consumption.