All bacteria reproduce asexually, and most rely on the transfer of genetic material by parasexual means to adapt through the acquisition of novel genotypes and to remove deleterious mutations. A handful of bacterial species do not undergo any such horizontal gene transfer (HGT), and evolve in a fully clonal manner. They gain novel genotypes solely through the accumulation of de novo mutations, and can only remove deleterious mutations by genome-wide selective sweeps. These clonally evolving bacteria include some of the most pathogenic species known to humans. As a consequence of their restricted means of increasing diversity and frequent purges of variation due to genome-wide sweeps, these species have very limited genetic diversity. The low resolution of the earliest molecular typing methods led to the members of these clonal species being considered identical clones, whose genetic diversity was negligible. The advent of whole genome sequencing (WGS) has revealed this assumption to be incorrect, by providing high-resolution characterisation of their genomes and revealing their existing diversity. The detailed data provided by WGS has so far been used primarily for tracking transmission and detecting drug resistance mutations, but it has potential as the basis for an exploration of population-level patterns in diversity and evolutionary selection. In this thesis, I develop a method of rapid and scalable analysis of these patterns that is suitable to large datasets, with thousands of genomes and thousands of genes. This allows for the full diversity of the population to be considered at once. I apply this method extensively to Mycobacterium tuberculosis, the best-studied clonal bacterial species and a widespread human pathogen. Lastly I compare the patterns in M. tuberculosis to three bacterial species which do undertake HGT, Campylobacter jejuni, Staphylococcus aureus and Neisseria meningitidis, to elucidate the patterns specific to clonally evolving bacteria.