Inferential summaries of tree estimates are useful in the setting of evolutionary biology, where phylogenetic trees have been built from DNA data since the 1960's. In bioinformatics, psychometrics and data mining, hierarchical clustering techniques output the same mathematical objects, and practitioners have similar questions about the stability and `generalizability' of these summaries. I will present applications of the Billera, Holmes, Vogtman (2001) distance to inferential problems both in the frequentist (bootstrap) and Bayesian contexts. I will compare the tree of trees representation to the Euclidean approximations of treespace made available through Multidimensional Scaling of the matrix of distances between trees. We also provide applications of the distances between trees to hierarchical clustering trees constructed from microarrays and phylogenetic trees of metagenomic data of bacteria in the gut. This talk contains joint work with John Chakerian and Alfred Spormann.