This thesis provides a comprehensive review for green routing problems (GVRPs) including 309 papers based on different perspectives, including variants of GVRP, methodology, objective functions, and so on. The methodological part of this study is quite fascinating for scholars. Therefore, we first proposed a new metaheuristic algorithm called Volleyball Premier League (VPL) inspired by the competition and interaction among volleyball teams during a season. And then, the multi-objective VPL (MOVPL) is extended based on the leader selection strategy. To show the applicability of the proposed approach, we introduce the sustainable vehicle routing problem (SVRP) as a realistic variant of the GVRP that can take into account the real operating conditions of urban freight distribution. A comprehensive framework based MOVPL, which is enhanced with the reference point approach, disruption operator, and an adaptive weight adjustment procedure, is proposed to solve a multi- objective mathematical model. We have also developed a new algorithm named shrinking procedure based on the Voronoi diagram called network shrinking procedure (NPS) to reduce the size of the network. Finally, an urban road network of Tehran city is also applied for further experimentation to show the validity of the proposed approach in connection with various perspectives. Based on the results of this study, the proposed algorithms, and modeling techniques, in comparison with the other well-known approaches, show to be both valid and efficient in finding the optimal solutions to the problem.