||Ensemble data sets appear in many domains, often as a result of a collection of solutions arising from the use of different parameters or initial conditions in simulations, measurement uncertainty associated with repeated measurements of a natural phenomenon, and inherent variability in natural or human events. Studying ensembles in terms of the variability between ensemble members can provide valuable insight into the generating process, particularly when mathematically modeling the process is complex or infeasible. Ensemble visualization is a way to understand the underlying generating model of data by studying ensembles of solutions or measurements. The objective of ensemble visualization is often to convey characteristics of the typical/central members, outliers, and variability among ensemble members. In the absence of any information about the generative model, a family of nonparametric methods, known as data depth, provides a quantitative notion of centrality for ensemble members. Data-depth methods also form the basis of several ensemble visualization techniques, including the popular Tukey boxplot. This dissertation explores data depth as a basis for visualizing various types of data for which existing visualization methods are either not directly applicable or present significant limitations. Such data include ensembles of three-dimensional (3D) isocontours, ensembles of paths on a graph, ensemble data in high-dimensional and inner-product spaces, and graphs. The contributions of this dissertation span the following three aspects of data-depth based visualizations: first, development of new data-depth methods that address the limitations of existing methods for computing center-outward order statistics for various types of ensemble data; second, development of novel visualization strategies that use existing and proposed data depth methods; and third, demonstration of the effectiveness of the proposed methods in real motivating applications.