Viral proteases play crucial roles in the life cycle and maturation of many viruses by processing the viral polyprotein after translation and in some cases cleaving host proteins associated with the immune response. The essential role of viral proteases makes them attractive therapeutic targets. In this thesis, I provide an introductory summary of viral proteases, their structure, mechanism, and inhibition, while the breadth of this thesis focuses on the Hepatitis C virus (HCV) NS3/4A and Zika virus (ZIKV) NS2B/NS3 viral proteases. HCV NS3/4A protease inhibitors (PIs) have become a mainstay in combination therapies. However, drug resistance remains a major problem against these PIs. In this thesis, I applied insights from the HCV substrate envelope (SE) model to develop strategies for designing PIs that are less susceptible to resistance. Also, I used the HCV NS3/4A protease as a model system to decipher the molecular mechanism and role of fluorination in HCV PIs potency and drug resistance. The drug design strategies described in this thesis have broad applications in drug design. The ZIKV is an emerging global threat, and currently, with no treatment available. In this thesis, I described the discovery, biochemical and antiviral evaluation of novel noncompetitive quinoxaline-based inhibitors of the ZIKV NS2B/NS3 protease. The inhibitors are proposed to interfere with NS2 binding to NS3, thereby preventing the protease from adopting the closed and active conformation. The inhibitors from this work will serve as lead compounds for further inhibitor development toward the goal of developing antivirals.