Recently we have witnessed the development of a fast growing body of research focused on vehicle routing and scheduling problem structures with time window constraints. It is the aim of this paper to survey the significant advances made for the following classes of routing problems with time windows: the single and multiple traveling salesman problem, the shortest path problem, the minimum spanning tree problem, the generic vehicle routing and scheduling problem, the pick-up and delivery problem including the dial-a-ride problem, the multi-period vehicle routing problem and the shoreline problem. Having surveyed the state-of-the-art in this area, we then offer some perspectives on future research.