In this article, we review both theoretical models and experimental results on the motion of micro-and nano-particles that are close to a fluid interface or move in between two fluids. Viscous drags together with dissipations due to fluctuations of the fluid interface and its physicochemical properties affect strongly the translational and rotational drags of colloidal particles, which are subjected to Brownian motion in thermal equilibrium. Even if many theoretical and experimental investigations have been carried out, additional scientific efforts in hydrodynamics, statistical physics, wetting and colloid science are still needed to explain unexpected experimental results and to measure particle motion in time and space scales, which are not accessible so far.