The vibrating conveyor is a machine with an obliquely oscillating trough that induces the saltation of particles. It is widely used for the transport of solid materials in industry. However, basic studies on the adhesive forces and fluid resistance that act on the particles have been neglected, and there have been few reports detailing the vibratory conveying of fine particles. This review summarizes the latest experimental and theoretical results on the behavior of fine particles on a two-dimensional oscillating plate. When a sufficiently high intensity of two-dimensional vibrations is applied to particles adhering to a plate, the particles become detached and bounce repeatedly. The external force in the tangential direction of the plate induces particle rolling, which decreases the particle-plate interaction force; as a result, even a relatively small external force will allow the particle to become detached from the plate. Furthermore, coarse single particles are transported by the repeated larger bounces with both forward and backward motions. On the other hand, fine particles can easily form agglomerated particles with low restitution and bounce slightly but only forward. Consequently, the transport velocity of agglomerated particles is greater than that of coarse single particles. These phenomena can be explained with a theoretical probability model and numerical simulation of the particle trajectory.