This dissertation presents experimental research investigating the behavior of particles on two different types of anisotropically curved liquid interfaces: cylinders and catenoids. The results are compared to the behavior predicted by theoretical models. Several types of liquids and many types of particles were examined. The size scale of the surfaces ranges from microns to millimeters, with nanometer and micron sized particles. Semi-cylinders, a few hundred microns in diameter, were made by creating a line of liquid on a surface. Three different fluids were used to create the semi-cylinders: Gallium, ionic liquids, and molten polystyrene (PS). Particle behavior on semi-cylinder liquid interfaces made from these materials was observed. Scanning electron microscopy (SEM) and optical microscopy were used to determine the location and assembly (related to particle attraction) of the particles on the surfaces of the fluids. PS semi-cylinders with silica particles were found to be the most promising experimental route, as PS will flow when heated above its Tg and will solidify when cooled to room temperature. As a solid, the PS surface is easily analyzed. Scanning force microscopy (SFM) was used on the PS semi-cylinders to image the deformation to the interface surrounding the particle, and a quadropolar deformation was found. PS catenoids, a few microns tall, were also investigated. The catenoids were produced by placing thin PS films heated above their Tg between two electrodes, separated from the surface of the film by a small air gap. A voltage was applied across the electrodes to create an electric field that produced electrohydrodynamic instabilities on the surface of the film that led to the formation of catenoids of molten PS that spanned the electrode gap. Semi-catenoids, several mm long, were also made from an ionic liquid by using chemically patterned wafers. SEM and optical microscopy were used to determine the particle location on the catenoid surfaces. The PS catenoids were found to be the most promising experimental system, and particles were observed to locate preferentially along the edges of the catenoid, instead of around the center as predicted.