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Vehicle Routing Problem (VRP) is a kind of combinatorial optimization problem with extensive application scenarios. At present, many methods for solving VRPs have been proposed, which can be divided into exact methods and heuristic methods. However, due to the complexity of VRPs, exact methods are limited extending to large scale VRPs, and heuristic methods usually needs manually tuning parameters. In recent years, with the development of machine learning and deep learning, many researchers have been successfully applied Learning Based Methods (LBM) to solve VRPs. In this paper, we give a brief review of LBMs for VRPs, including end-to-end approaches and iterative improvement approaches. Then through experimental results, we analyzed the advantages and disadvantages of the two types of approaches. Finally, we summarize the characteristics of them, and look forward to the future research directions.