In metropolitan cities, it is very complicated to govern the optimum routes for garbage collection vehicles due to high waste production and very dense population. Furthermore, wrongly designed routes are the source of wasting time, fuel and other resources in the collection of municipal trash procedure. The Vehicle Routing Problem (VRP) published between 2011 and 2023 was systematically analysed. The majority of the surveyed research compute the waste collecting problems using metaheuristic approaches. This manuscript serves two purposes: first, categorising the VRP and its variants in the field of waste collection; second, examining the role played by most of the metaheuristics in the solution of the VRP problems for a waste collection. Three case study of Asia continent has been analysed and the results show that the metaheuristic algorithms have the capability in providing good results for large-scale data. Lastly, some promising paths ranging from highlighting research gap to future scope are drawn to encourage researchers to conduct their research work in the field of waste management route problems.