Viruses are the most abundant biological entities on Earth, infecting all types of cellular organisms. Yet less than 1% of the virosphere on our planet has been characterized to date. Viruses are both an important driver of bacterial evolution and have significant implications for human health, therefore understanding the relative contributions of various evolutionary forces in shaping their genomic landscapes is of critical importance both mechanistically as well as clinically. In my thesis I use computational genomic approaches to gain novel insights into bacteriophage and human cytomegalovirus evolution. In my first two chapters and associated appendices I characterized the complete genomes of the Cluster P bacteriophage Phegasus and Cluster DR bacteriophage BiggityBass, whose isolation hosts were Mycobacterium smegmatis mc²155 and Gordonia terrae CAG3, respectively. I also determined the bacteriophages' phylogenetic placement and computationally inferred their putative host ranges. For my fourth chapter I assessed the performance of several of these computational host range prediction tools using a dataset of bacteriophages whose host ranges have been experimentally validated. Finally, in my fifth chapter I reviewed the key parameters for developing an evolutionary baseline model of another virus, human cytomegalovirus.