Shared water resource systems spark a number of conflicts related to their multi sectorial, regional, and intergenerational use. They are also vulnerable to a myriad of uncertainties stemming from changes in the hydrology, population demands, and climate change. Planning and management under these conditions are extremely challenging. Fortunately, our capability to approach these problems has evolved dramatically over the last few decades. Increased computational power enables the testing of multiple hypotheses and expedites the results across a range of planning alternatives. Advances in flexible multi-objective optimization tools facilitate the analyses of many competing interests. Further, major shifts in the way uncertainties are treated allow analysts to characterize candidate planning alternatives by their ability to fail or succeed instead of relying on fallible predictions. Embracing the fact that there are indeterminate uncertainties whose probabilistic descriptions are unknown, and acknowledging relationships whose actions and outcomes are not well-characterized in planning problems, have improved our ability to perform diligent analysis. Multi-objective robust planning of water systems emerged in response to the need to support planning and management decisions that are better prepared for unforeseen future conditions and that can be adapted to changes in assumptions. A suite of robustness frameworks has emerged to address planning and management problems in conditions of deep uncertainty. That is, events not readily identified or that we know so little about that their likelihood of occurrence cannot be described. Lingering differences remain within existing frameworks. These differences are manifested in the way in which alternative plans are specified, the views about how the future will unfold, and how the fitness of candidate planning strategies is assessed. Differences in the experimental design can yield diverging conclusions about the robustness and vulnerabilities of a system. Nonetheless, the means to ask a suite of questions and perform a more ambitious analysis is available in the early 21st century. Future challenges will entail untangling different conceptions about uncertainty, defining what aspects of the system are important and to whom, and how these values and assumptions will change over time.