Sustainable logistics aims to balance economic efficiency, environmental responsibility, and social well-being in supply chain operations. This study explores the use of Variable Neighborhood Search (VNS), a metaheuristic optimization method, in addressing sustainable logistics challenges and provides insights into the potential it has to support them by delivering efficient solutions that align with global sustainability goals. The review identifies key trends, including a significant increase in research since 2019, with a strong focus on routing, scheduling, and location problems. Hybrid approaches, combining VNS with other methods, and multiobjective optimization to address trade-offs between sustainability goals are prominent. The most frequently applied VNS versions align closely with those commonly used in the broader literature, reflecting similar adoption proportions. In recent years, a noticeable increase in studies incorporating adaptation mechanisms into VNS frameworks has emerged. This trend is largely driven by the growing influence of Artificial Intelligence approaches across numerous fields of science and engineering, highlighting the need for more dynamic and intelligent optimization techniques. However, important research gaps remain. These include limited consideration of uncertainty and dynamic logistics systems, underrepresentation of social sustainability, and a lack of standardized benchmarks for comparing results. Future work should address these challenges and explore emerging applications.