Clustering is the process of finding underlying group structure in data. As the scale of data collection continues to grow, this “big data” phenomenon results in more complex data structures. These data structures are not always compatible with traditional clustering methods, making their use problematic. This thesis presents methodology for analyzing samples of four-way and higher data, examples of these more complex data types. These data structures consist of samples of continuous data arranged in multidimensional arrays. A large emphasis is placed on clustering this data using mixture models that leverage tensor-variate distributions to model the data. Parameter estimation for all these methods are based on the expectation-maximization algorithm. Both simulated and real data are used for illustration. / Thesis / Doctor of Science (PhD)