Explore the evolution of distance-based phylogenetics in this comprehensive tutorial from the Computational Genomics Summer Institute. Delve into the foundations of weighted tree metrics and additive metric spaces before examining methods for obtaining distances, including Hamming distance and statistical distance correction. Learn about inferring trees from additive distances using the naive quartet approach and practical methods with strong asymptotic theoretical results. Discover applications in phylogenetic placement, such as ecological sample identification in microbiome studies and genome skimming. Investigate two-step summary methods and the cutting-edge use of deep learning for phylogenetic placement (DEPP). Gain insights into current challenges and future directions in the field, with references to key research papers for further study.