Viruses can be attributed to many devastating human diseases. In this thesis I present quantitative methods and analysis of infections of vesicular stomatitis virus (VSV) in cell culture environments. The work presented here reveals new information about VSV infection and suggests future directions for quantitative study of viral infections. Quantitative data collection and analysis in Chapter 2 reveal that the mRNA production rate is dependent only on viral genomes, suggesting that viral polymerases are in excess. This work suggests that VSV is able to establish a robust infection in multiple cellular environments. In Chapter 3 I present a large scale simulation and simulation environment developed to predict the outcome of infections of multiple strains of VSV in cell culture. The simulation reveals that viral genome replication is limited by the presence of the nucleocapsid protein, the catalyst for genome replication. Finally, in Chapter 4 I present quantitative analysis of VSV populations using RNA sequencing. This work shows that RNA sequencing is an unbiased tool that can be used to detect, identify, and quantify defective interfering particles in a virus population. Together this work shows that quantitative analysis of biological systems can reveal new biology. Quantitative techniques are necessary for developing predictive models of viral infections, which will lead to the rational design of anti-viral treatments.