Inferring evolutionary histories, or phylogenetic trees, has important applications in biology, criminology and public health. However, phylogenetic trees are complex, non-Euclidean objects. While our mathematical, algorithmic, and probabilistic understanding of the behavior of trees in their metric space is mature, statistical infrastructure is relatively underdeveloped. This thesis proposes inferential and exploratory statistical methods for the analysis of tree-valued data. The inferential method is a confidence set for the Fréchet mean of a distribution with support on the metric space of phylogenetic trees. Two exploratory methods are proposed for visualizing collections of trees, which rely on similar tools to the confidence set procedure. Finally, some results relating to modeling estimates of trees are given, and related open problems are discussed.