To enter and infect cells, viruses must overcome the barrier presented by the cell membrane. Enveloped viruses, which possess their own lipid bilayer, fuse their viral membrane with the cell membrane. Non-enveloped viruses, whose outer surface is composed of proteins, penetrate through the hydrophobic interior of the cell membrane. Viruses accomplish the processes by coupling conformational changes in viral "entry proteins" to membrane disruption. This dissertation investigates the membrane disruption mechanisms of rotavirus, a non-enveloped virus, and vesicular stomatitis virus (VSV), an enveloped virus. Rotavirus uses proteins of its outer capsid to penetrate the membrane and deliver a transcriptionally-active core particle into the cell cytoplasm. \(VP5^*\), an outer capsid protein, undergoes a foldback rearrangement that translocates three clustered hydrophobic loops by \(\sim 180^{\circ}\). This rearrangement resembles the foldback rearrangements of enveloped virus fusion proteins. In the first half of my dissertation, I show that the hydrophobicity of the \(VP5^*\) apex is required for membrane disruption during rotavirus cell entry by mutating hydrophobic residues within the loop to hydrophilic residues. One particular mutation diminishes liposome interaction by the protein, blocks membrane penetration by virus particles in cells, and reduces particle infectivity by 10,000-fold. VSV uses its fusion protein, G, to fuse at low pH. Unlike other viral fusion proteins, pH-induced conformational changes in G are reversible. In the second half of my dissertation, I measure the fusion kinetics of individual VSV particles using a single-particle fusion assay previously developed for influenza virus. I find that hemifusion by VSV consists of at least two steps, an initial step that is pH-dependent and reversible, and a second step that is pH-independent. At low pHs, the second step becomes the sole rate-limiting step. I also show that at pH 6.6, the VSV particle enters a stable intermediate state that binds tightly to membranes but does not precede to fusion. This dissertation uses a variety of experimental approaches to arrive at a more detailed understanding of how viruses use their entry proteins to either penetrate or fuse with the cell membrane.