Many plant pathogens, including those in the lineage of the Irish potato famine organism Phytophthora infestans, evolve by host jumps followed by specialization. However, how host jumps affect genome evolution remains largely unknown. To determine the patterns of sequence variation in the P. infestans lineage, we resequenced six genomes of four sister species. This revealed uneven evolutionary rates across genomes with genes in repeat-rich regions showing higher rates of structural polymorphisms and positive selection. These loci are enriched in genes induced in planta, implicating host adaptation in genome evolution. Unexpectedly, genes involved in epigenetic processes formed another class of rapidly evolving residents of the gene-sparse regions. These results demonstrate that dynamic repeat-rich genome compartments underpin accelerated gene evolution following host jumps in this pathogen lineage.