Research on dynamic and stochastic vehicle routing problems received increasing interest in the last decade. It considers a novel problem class, aiming at an appropriate handling of dynamic events combined with the incorporation of stochastic information about possible future events. This survey summarizes recent literature in this area. Besides the classification according to the available stochastic information, a new classification based on the point in time where substantial computational effort for determining decisions or decision policies arises, is introduced. Furthermore, the difference in solution quality is analyzed between approaches which consider either purely dynamic or stochastic problems compared to those which consider both, stochastic and dynamic aspects. A graphical representation demonstrates the strength of the reviewed approaches incorporating dynamic and stochastic information. The survey also gives an overview on the intensity of research for the different problem classes and its benefit in recent years. Finally, guidelines and promising directions for further research are presented.