Ensemble datasets are being increasingly seen in a range of domains. Such datasets often appear as a result of a collection of solutions recorded from simulation runs with different parameters/initial conditions, as well as precision uncertainty associated with repeated measurements of a natural phenomenon. Studying ensembles in terms of the variability between members can provide valuable insight into the generating process; particularly when mathematically modeling the process is complex or infeasible. Ensemble visualization can be a powerful way to study the generating process by analyzing ensembles of solutions or possible outcomes. In ensemble visualization, key interests include understanding the typical/atypical members as well as variability in the ensemble. In absence of any information about the underlying generative model, data depth, a family of nonparametric methods from descriptive statistics, is able to quantify the notion of centrality and provide center-outward order statistics for ensembles. The goal of the proposed dissertation is to explore novel applications for existing depth based visualization methods, and to develop new advantageous visualizations—and associated methods to compute depth—for ensembles of various data types—namely, 3D isocontours, paths on a graph, nodes on a graph, graphs, and data in inner product spaces.