Optimization under uncertainty has been a well-studied field, with renewed interest generated in this field in the past four decades. This paper is both practical and expository, its purpose is to: discuss the process of generating robust solutions, highlight issues that arise in practice, and discuss ways to address such issues. For illustrative purposes, we study three different, commonly adopted, approaches for optimization under uncertainty (chance-constrained programming, robust optimization and conditional value at risk); and apply these approaches to three real-world application-based case studies. Our case studies are chosen to span a variety of problem characteristics. For each case study, we discuss the applicability of each of the three approaches, practical issues that arose during application, and robustness and further characteristics of the subsequent solutions. We point out associated advantages and limitations, and illustrate the gap between the theoretical and actual performance of these approaches for each case study. We also discuss how some of the discovered limitations can be overcome using extensions of the approaches or through a better understanding of the data. We conclude by summarizing common and generalizable insights obtained across the three case studies. Our findings suggest the effectiveness of solutions is dependent on: the methods, the size of the problem, the underlying pattern of uncertainty in data, and the metrics of interest. While we provide some guidelines to identify the most suitable approach to a given problem, our experience matches theory to suggest that under carefully tuned parameters accompanied by simulation, the different approaches can generate results that are similar and provide comparable tradeoffs between the mean and robustness metric. However, this could also require considerable tuning especially with experience, and we provide some guidelines to achieve such results. This illustrates that generating high quality robust solutions is both an art and a science.