Robust optimization is a mathematical programming-based approach to decision-making under uncertainty that is receiving wide attention because of its modeling power, computational tractability and rich theoretical properties. In this talk, we will introduce the robust optimization concept and present some of our recent theoretical and algorithmic contributions to extend its applicability towards two-stage (dynamic) decision-making problems. We will then present its application in addressing the solution of some fundamental "vehicle routing" problems that arise in the context of distribution operations in industrial and commercial supply chains. Specifically, we will present models and solution algorithms for the tactical planning of multi-period operations under customer order uncertainty, and (time permitting) for the operational routing of large-scale vehicle fleets under demand uncertainty.