Anatomical trees appear as transportation systems distributing blood, water or air. Due to their critical role, statistics on populations of trees is essential to understanding disease. This is difficult due to anatomical variation in branching structure across subjects. I will present a geometric tree-space framework for leaf-labeled trees, discuss how statistics can be defined and performed in tree-space, and present applications to anatomical labeling of airway trees and large-scale statistics on the effect of Chronic Obstructive Pulmonary Disease on airway trees.