What will be tomorrow's big cities objectives and challenges? Most of the operational problems from the real world are inherently subject to uncertainty, requiring the decision system to compute new decisions dynamically, as random events occur. In this thesis, we aim at tackling an important growing problem in urban context: online dynamic vehicle routing. Applications of online vehicle routing in the society are manyfold, from intelligent on demand public transportation to sameday delivery services and responsive home healthcare. Provided the current state at some moment of the day, which are the best vehicle actions such that the expected number of satisfied requests is maximized by the end of the operational day? How can we minimize the expected average intervention delays of our mobile units? Optimization under uncertainty is definitely not a recent issue. Thanks to evolution of both theoretical and technological tools, our ability to face the unknown constantly grows. However, most of the interesting problems remain extremely hard, if not impossible, to solve. There is still a lot of work. Generally speaking, this thesis explores some fundamentals of optimization under uncertainty. By integrating a stochastic component into the models to be optimized, we will see how it is in fact possible to create anticipation. Michael Saint-Guillain obtained his PhD in Computer Sciences, jointly with Université catholique de Louvain (UCLouvain, Belgium) and the Institut National des Sciences Appliquées de Lyon (INSA-Lyon, France), in 2019. First focused in dynamic and stochastic VRPs, its interested generalized to operations management and decision making under uncertainty. At the time of writing, he is working on the application of probabilistic models for robust operation planning, in the context of biotechnology manufacturing and space exploration.