Evolutionary relationships between a group of organisms are commonly summarized in a phylogenetic (or evolutionary) tree. The goal of phylogenetic inference is to infer the best tree structure that represents the relationships between a group of organisms, given a set of observations (e.g. molecular sequences). However, popular heuristics for inferring phylogenies output tens to hundreds of thousands of equally weighted candidate trees. Biologists summarize these trees into a single structure called the consensus tree. The central assumption is that the information discarded has less value than the information retained. But, what if this assumption is not true? In this dissertation, we demonstrate the value of retaining and studying tree collections. We also conduct an extensive literature search that highlights the rapid growth of trees produced by phylogenetic analysis. Thus, high performance algorithms are needed to accommodate this increasing production of data. We created several efficient algorithms that allow biologists to easily compare, store and share tree collections over tens to hundreds of thousands of phylogenetic trees. Universal hashing is central to all these approaches, allowing us to quickly identify the shared evolutionary relationships contained in tree collections. Our algorithms MrsRF and Phlash are the fastest in the field for comparing large collections of trees. Our algorithm TreeZip is the most efficient way to store large tree collections. Lastly, we developed Noria, a novel version control system that allows biologists to seamlessly manage and share their phylogenetic analyses. Our work has far-reaching implications for both the biological and computer science communities. We tested our algorithms on four large biological datasets, each consisting of 20; 000 to 150; 000 trees over 150 to 525 taxa. Our experimental results on these datasets indicate the long-term applicability of our algorithms to modern phylogenetic analysis, and underscore their ability to help scientists easily exchange and analyze their large tree collections. In addition to contributing to the reproducibility of phylogenetic analysis, our work enables the creation of test beds for improving phylogenetic heuristics and applications. Lastly, our data structures and algorithms can be applied to managing other tree-like data (e.g. XML).