When two fluids come into contact an interface is formed between them. The surface tension of this interface plays an important role in determining the shape of the surface and can be lowered by the presence of surfactants. In dynamic interfacial fluid problems surface tension gradients due to surface convection of the surfactant can develop. These gradients result in Marangoni stress on the surface which affects surface velocities and thus bulk fluid velocities. These flows are relevant in enhanced oil recovery; dip and spin coating technologies; condensate formation on heat exchangers; emulsions in polymerization, biofuels, pharmaceuticals and food processing; and any number of microfluidics technologies, to name a few examples. The vast applications make the understanding of surface tension effects on interfacial flows important. A theoretical understanding exists for how surface tension gradients and Marangoni stress affect interfacial fluid flows, but direct comparisons between experiments and theory is less common in the literature. In this thesis two fluid dynamics problems involving drops are studied. In the first an aqueous drop containing surfactant is placed in a horizontal rotating cylindrical tank half-filled with oil. A film of oil forms between the drop and wall, and the addition of surfactant affects the film thickness, drop shape, and onset of drop breakup. The second problem involves an aqueous drop containing surfactant settling in oil under gravity where surface tension gradients affect the terminal velocity or drag of the drop. Using in-house surface tension measurements, surfactant adsorption and desorption models are developed. These models are then used in analytical and numerical analyses of the aforementioned fluid dynamics problems and compared to experiments. The results demonstrate the potential to use experimentally determined surfactant transport parameters to explain and in some cases predict experimental observations.