The impact of short-range repulsive interactions between nuclei on the evolution of a phase transformation is studied in order to describe quantitatively the kinetics of the transformation and to characterize systematically the resulting microstructures. For these purposes both computer simulation and analytical methods are employed in order to investigate an idealized, two-dimensional model of nucleation and growth wherein nuclei contained in a background phase (e.g., liquid) interact via a "hard-core" repulsion, a prototype for systems with a variety of possible interactions. Several quantities, including the dynamic area and perimeter fractions as well as the distribution of coalesced grain areas, are calculated. It is found, for example, that the temporal evolution of the system differs markedly from that in which the nuclei are spatially uncorrelated, particularly as the core diameter becomes large relative to the characteristic internuclear separation for noninteracting nuclei, and an approximate, analytic description of this behavior is obtained. Finally, the morphologies of the grains constituting the transformed microstructures are linked with the range of the internuclear interaction.