Bacterial genomes vary in sequence due to mutations but also vary in their gene content and order due to horizontal gene transfer. Whether the variation in gene content and order, known as the accessory genome, is typically neutral, nearly neutral or adaptive is still the subject of debate – different theoretical arguments support all three scenarios. The availability of large sample collections across many thousands of bacterial species offers the opportunity to bring data to bear on this question. I will first present methods being developed in my group to make it possible to analyse collections of millions of genomes. Using these approaches, I will then show how a mechanistic model of gene gain and loss can be fitted to different pathogen species to determine whether their accessory genome shows signals of adaptation. Finally, I will show how transformer-based AI architectures can learn gene content and ordering across even more species, giving another way to look at this problem.