Enzymes that catalyze DNA and RNA replication are biologically important and provide examples to understand enzyme specificity as the correct substrate and alternate substrates are well known. The DNA polymerase from bacteriophage T7 has been a model system for understanding high-fidelity DNA replication, yet outstanding questions remain about the controversial nucleotide induced conformational change. I developed methods to directly measure the conformational change by site specifically incorporating a fluorescent unnatural amino acid into the enzyme at a position that gives a fluorescence signal upon nucleotide binding. In addition, I developed high throughput methods to analyze kinetic samples by capillary electrophoresis to assist in the kinetic analysis of DNA replication. Kinetic studies show that the conformational change is the primary determinant of specificity at the polymerase active site. I also characterized the enzyme’s 3’--5’ proofreading exonuclease activity and showed that the enzyme has multiple opportunities to correct mistakes during replication. I also used molecular dynamics simulation methods to propose a structure of the proofreading exonuclease editing complex. While finishing studies on the T7 DNA polymerase, the SARS-CoV-2 pandemic devastated the world. I used techniques developed in my previous studies to characterize the RNA dependent RNA polymerase (RdRp) from SARS-CoV-2, a prime target for antiviral drugs to stop replication of the virus. I developed methods to express the tag free complex in E. coli and subsequent purification to give highly active enzyme, which for the first time met standards for physiologically relevant activity. I characterized the pre-steady state kinetics of UTP and ATP incorporation and found that the enzyme catalyzes nucleotide incorporation at a fast rate, sufficient to replicate the 30 kb viral genome in less than 2 minutes. The ATP analog Remdesivir triphosphate, the only FDA approved treatment for COVID-19, was then studied to calculate the discrimination relative to ATP. We found that Remdesivir is incorporated more efficiently than ATP and acts as a delayed chain terminator, although this termination can be partially overcome by incubation with high nucleotide concentrations. Cryo-EM was used to determine the structure of the Remdesivir stalled RdRp complex and we found that the translocation step was inhibited after incorporation of 3 Remdesivirs due to a steric block between Remdesivir and the enzyme.