This thesis discusses the role of analysis in the application of molecular dynamics (MD) simulations for studying phenomena at an atomic level of detail. Many interesting questions can be asked of the physical world: How do proteins fold? Are there two liquid phases of supercooled water? How does a drug inhibit an enzyme? Many of these questions, however, are not quantitatively specific, meaning that the answers depend on scientists' interpretation. Researchers tend to describe these phenomena through hand-chosen functions, or order parameters, that are based on physical intuition. However, there is an immense amount of information contained in a large-scale simulation that is typically not used. Here, we attempt to illustrate the usefulness of data-driven analysis in the study of physical phenomena with MD. In all cases, the strategy begins by reformulating the nebulous physical questions into a specific and quantitative question, which can be used to derive an appropriate unsupervised learning method for the given problem. This strategy rests on physical intuition, because the problem formulation must be done in a physically meaningful way, but the advantage is that the specific solutions are driven by the data itself, allowing for interesting phenomena to be discovered rather than required to be known a priori.