Background: The objective of this literature review is to systematically explore the supply chain (SC)-related issues of additive manufacturing (AM)-based production processes. For SC sustainability, efficiency, and performance improvements, the adoptation of disruptive technologies like AM plays a vital role, because the product’s SC benefits in terms of reduced total lead time and costs. Methods: To explore the state-of-the-art influences of AM on the SC in this study, 978 papers published in peer-reviewed journals from 2004 to 2023 were retrieved, and 70 of these were identified as the most relevant and then reviewed. Results: As an outcome, the results of this review paper indicated a lack of documented studies in developing countries and, as a result, limited research works, for instance, in fashion industries were observed. In addition, AM best practices in the SC context have been identified and categorized as cost-related, time-related, inventor-related, as well as energy-, waste-, and environment-related factors, SC efficiency factors, and flexibility, marketing, and manufacturing-related factors. Conclusions: By identifying these categories, the study aims to contribute to the efforts of transforming traditional manufacturing into AM-based processes, for which a framework for the AM SC implementation is developed. In summary, the systematic review indicated that further research work is needed on the impacts of the identified AM best practices on SC performance.