This dissertation discusses recent developments in single-particle tracking (SPT) assays and computational tools for studying the interaction between viruses and lipid membranes. Lipid membranes of host cells are effective barriers against foreign entities, but viruses have evolved strategies to bind to and penetrate through these membranes. The infection process involves a series of virus-host interactions such as 1) activation of viral proteins via host cell proteases, 2) binding of virus proteins to specific host cell receptors, 3) conformational changes of viral fusion proteins near the cell membrane, and 4) fusion of the cell and viral membranes. Building assays that can study these interactions is useful for expanding our knowledge on viruses and confirming the activity of antiviral compounds. With the combined usage of high-resolution microscopy and supported lipid bilayers, individual viruses can now be tracked as they undergo sequential steps of the virus infection process. Yet, the utility of this assay is limited by experimental design, image processing, and data analysis challenges. We have thus developed 1) an assay that can trigger virus membrane fusion rapidly, 2) a stochastic simulation model that explains major kinetics steps of the fusion process, 3) an image restoration algorithm that reveals virus particles in noisy SPT videos, and 4) a kinetic model that describes the "adhesion-strengthening" mechanism that viruses use to stably bind to membranes. We have tested the utility of these tools as we dissected the kinetics steps involved with the influenza virus and parvovirus infection process.