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Many real-life applications of the vehicle routing problem (VRP) occur in scenarios subject to uncertainty or dynamic conditions. Thus, for instance, traveling times or customers’ demands might be better modeled as random variables than as deterministic values. Likewise, traffic conditions could evolve over time, synchronization issues should need to be considered, or a real-time re-optimization of the routing plan can be required as new data become available in a highly dynamic environment. Clearly, different solving approaches are needed to efficiently cope with such a diversity of scenarios. After providing an overview of current trends in VRPs, this paper reviews a set of heuristic-based algorithms that have been designed and employed to solve VRPs with the aforementioned properties. These include simheuristics for stochastic VRPs, learnheuristics and discrete-event heuristics for dynamic VRPs, and agile optimization heuristics for VRPs with real-time requirements.