Particles can be adsorbed to liquid-fluid interface to minimize interfacial energy. The adsorbed particles interact in many ways. There has been a lot of theoretical predictions as well as experimental measurements of the interaction potential between particles confined at interfaces. Experimentally, we track multiple particles using optical microscope image processing of isolated pairs of particles and of more concentrated systems. Statistical methods were implemented to compute microparticle interaction forces from tracking data. The accuracy of different methods were tested with Monte Carlo simulation, which showed that care is needed to avoid artifacts. Our measurements confirmed the absence of significant pair-interactions among charged microparticles and liquid droplets at flat air-water interfaces. At the interface between water and a fluorocarbon, however, we observed strong interactions that cannot be explained by capillary interactions among neutral particles. Theoretically, we focused on the capillary interaction mediated by the curvature of interface. The perturbation to a cylindrical interface upon adsorption of a single spherical particle is studied first. We present an analytical model of the interfacial shape and energy upon adsorption of a single particle, and then calculate the interaction between two particles. Based on our result for a cylindrical interface, we propose a general formula for the force on a particle on a curved interface having constant mean curvature (i.e., not subject to an external forces). This study provides an important step toward understanding the interactions among interfacial particles.