Abstract: We report on the ordering and dynamics of interacting colloidal particles confined by a parabolic potential. By means of Brownian dynamics simulations, we find that by varying the magnitude of the trap stiffness, it is possible to control the dimension of the system and, thus, explore both the structural transitions and the long-time self-diffusion coefficient as a function of the degree of confinement. We particularly study the structural ordering in the directions perpendicular and parallel to the confinement. Further analysis of the local distribution of the first-neighbors layer allows us to identify the different structural phases induced by the parabolic potential. These results are summarized in a structural state diagram that describes the way in which the colloidal suspension undergoes a structural re-ordering while increasing the confinement. To fully understand the particle dynamics, we take into account hydrodynamic interactions between colloids; the parabolic potential constricts the available space for the colloids, but it does not act on the solvent. Our findings show a non-linear behavior of the long-time self-diffusion coefficient that is associated to the structural transitions induced by the external field. (C) 2015 AIP Publishing LLC.