Antiviral APOBEC3 (A3) enzymes restrict viral activity through hypermutations of cytosine but can also be drivers of viral diversity. When new viruses emerge through spill over events or viral variants evolve within the human population it is unclear how human A3 enzymes will interact with viral genomes. Three recent public health examples illustrate the need for additional knowledge and analysis of A3s. First, initial studies from the 2022 Mpox outbreak identified numerous C-to-T mutations, a typical signature of A3 activity. However, predicting the potential of A3-mediated mutagenesis in Mpox was not attempted. Second, following the Covid-19 pandemic, A3s were identified as a contributing mutator of the causative virus SARS-CoV-2 and many machine learning tools have been developed to model SARS-CoV-2 evolution, but there is still no model combining the two. Third, A3s are important spill over barriers between species and yet A3 characterization and enzymatic activity is understudied in non-model species known to harbor zoonotic diseases. Bats have unique but diverse immunity and host many zoonotic diseases without clinical symptoms. Some bats are known to host coronaviruses and are thought to be the original hosts of SARS-CoV and SARS-CoV-2. Still, only 7 of over 1400 different bat species A3 enzymes have been studied and, in some cases, their enzymatic activity or relationship to bat immunity is not yet known. In this dissertation these three major knowledge gaps are addressed. We used mathematical and computational techniques to study A3 interactions with the viruses Mpox and SARS-Cov-2, and A3 evolution in bats. We identified Mpox genes with high mutation potential using computational algorithms and trained a machine learning model to learn A3 specific substitution rate patterns in early SARS-CoV-2 genomes. We built a pipeline to extract bat A3 catalytic region genes in unannotated genomes, used phylogenetic comparative algorithms to infer the evolutionary dynamics of A3 in 102 bats, and developed a Bayesian hierarchical model to relate A3 evolutionary events to bat-hosted virus count. The number of catastrophic disease outbreaks and pandemics caused by zoonotic diseases is thought to continue to increase, so studying viruses and proteins which act on them is critical.