Over the last several years, interest in computing and then using large-scale phylogenies has increased for multiple reasons, including basic science (how did life evolve on earth) and applications in biomedicine and public health (e.g., understanding the evolution of SARS-Cov-2). The estimation of these large phylogenies, wiith potentially millions of leaves, presents fascinating mathmetical, statistical, and computational challenges, ranging from computing multiple-sequence alignments, developing effective heuristics to NP-hard optimization problems (e.g., maximum likelihood tree estimation) on large datasets), estimating species trees from genome- scale data while addressing biological causes for heterogeneity (e.g., gene duplication and loss and incomplete lineage sorting) across the genome). There are also many fascinating and difficult problems that have to do with “post-tree” analyses, such as rooting gene trees and species trees, or estimating branch lengths in species trees and dates at internal nodes, that are needed for many down-stream analyses. In this talk I will describe progress on these questions, and I will also present some open problems where new techniques are needed.