Bayesian phylogenetic inference usually explore the posterior distribution of trees via Markov Chain Monte Carlo methods, however assessing uncertainty and summarizing distributions remains challenging for these types of structures. In this talk I will first introduce a distance metric on the space of unlabeled ranked tree shapes and genealogies. I will then use it to define several summary statistics such as the Fréchet mean, variance, and interquartile sets. I will then provide an efficient combinatorial optimization algorithm for computation and show the applicability of our summaries for studying popular tree distributions and for comparing the SARS-CoV-2 evolutionary trees across different locations during the COVID-19 epidemic in 2020. I will extend the distance definition to the space of labeled ranked phylogenies and unlabeled phylogenetic networks and discuss potential applications of the distances for inference.