The addition of natural components with functional properties in novel food formulations confers one of the main challenges that the modern food industry is called to face. New EU directives and the global turn to circular economy models are also pressing the agro-industrial sector to adopt cradle-to-cradle approaches for their by-products and waste streams. This review aims to present the concept of “sustainable functional compounds”, emphasizing on some main bioactive compounds that could be recovered or biotechnologically produced from renewable resources. Herein, and in view of their efficient and “greener” production and extraction, emerging technologies, together with their possible advantages or drawbacks, are presented and discussed. Μodern examples of novel, clean label food products that are composed of sustainable functional compounds are summarized. Finally, some action plans towards the establishment of sustainable food systems are suggested.