Biologists have been interested in reconstructing the history of biological diversification on Earth ever since the time of Darwin. This field of study has since become known as phylogenetics. Phylogenetics was revolutionized starting in the early 1980s with the application of formal statistical approaches to inference using genetic data. Technical advances in the mid-2000s made it possible to sequence full genomes much more cheaply and quickly than ever before, which has radically increased the amount of available data. However, many challenges and open questions remain about how best to handle the scale and complexity of full-genome data in likelihood-based statistical frameworks. In this talk, I will discuss some strategies that my lab is pursuing to more efficiently and effectively reconstruct the evolutionary past from genomic data using Bayesian methods.