Some of the most ecologically-significant pathogens of plants, animals and marine life come from two groups of filamentous eukaryotes; the oomycetes and the fungi. Although similar in morphology and ecological niche, the two groups are only very-distantly related in terms of evolutionary history. The oomycetes are underresearched in evolutionary science, despite their historical and contemporary impact on food and environmental security. In contrast, fungi themselves are probably the most densely studied and sequenced group of organisms in evolutionary science outside of bacteria. This thesis is a collection of five published computational studies of the evolutionary biology of oomycetes and fungi. The first study is a systematic investigation of bacterial horizontal gene transfer into plant pathogenic oomycete species, which identifies 5 potential HGT events from prokaryotes into multiple oomycetes. The second study is a reconstruction of the evolutionary history of the oomycetes using wholegenome data from 37 species, which supports the larger groups within the oomycetes class but suggests that some exemplar oomycete genera are paraphyletic. Taking advantage of the abundance of genomics data available for all major fungal phyla, the third study reconstructs the evolutionary history of 84 fungal species using seven different phylogenomic techniques and critically evaluates each technique for accuracy, speed and other criteria. The fourth study looks at the pangenomes of four model fungal species, and compares the evolution of genomic variation, virulence and environmental adaptation within each species. The final study presents a refined iteration of the methodology used in the previous pangenome study as a self-contained software package and demonstrates the software’s capabilities through pangenome analysis and re-analysis of both model and non-model fungal species. Together, these studies cover a breadth of molecular evolution, comparative genomics, phylogenomics and pangenomics research for two similar, but evolutionarily-distinct groups of important microscopic eukaryotes.