The formation and dynamics of vortical structures in two-dimensional flows are investigated numerically and theoretically. Localized initial distributions with random fluctuations are in general found to evolve into large scale vortical structures. If the initial perturbation contains a linear momentum the development into propagating dipolar structures is observed. This development is discussed by employing self-organization principles. The detailed structures of the evolving dipoles depends on the initial condition. It seems that there are no unique dipolar solutions, but a large class of solutions is possible. However, it is argued that the gross properties of the dipoles do not depend critically on the detailed structure. The vortical structures are found to trap particles and convect them over distances much larger than the scale size of the structure. Two examples of trapping/detrapping of particles are shown. The trapping of particles by a decaying, expanding dipolar vortex and the detrapping of particles during the merging of two Like-signed monopolar vortices.