The purpose of this paper is to update recent research of the fleet size and mix vehicle routing problem (FSMVRP), the heterogeneous fleet vehicle routing problem (HFVRP), and the extensions in a form of a literature review. In this paper, four major components of the problem: classification, considerable input data characteristics, decision making approaches, and heuristic and meta-heuristics algorithms are discussed. The comprehensive overview of the heterogeneous vehicle routing problem which puts a special emphasis on robustness approach is concluded and demonstrated in a simplified structure which has never been presented before. New potential research areas resulting from the survey are suggested in the final section.