Phase coarsening, also termed Ostwald ripening, is generally thought to be a slow, diffusion-controlled process which occurs subsequent to phase separation under extremely small under- or over-saturation levels. The theory due to Lifshitz, Slyzov, and Wagner (LSW), which predicts the coarsening kinetics and the particle distribution function is applicable to dilute systems only, in which particle-particle interactions are unimportant. Most practical systems, however, have large enough volume fractions of the dispersed phase to violate the essential assumptions of LSW theory. Recent progress will be described on simulating Ostwald ripening in randomly dispersed, high volume fraction systems. A fast algorithm for solving the multiparticle diffusion problem (MDP) will be described, permitting simulation of coarsening dynamics by cyclic time-stepping and updating the diffusion solution for large random particle arrays. The rate constants, controlling the growth of the average particle, and the particle distribution functions were obtained by numerical simulations up to a volume fraction of 0.55. A new statistical mechanics theory has now been developed which reproduces the MDP simulation data accurately, and finally makes clear how the linear mean-field approximations employed by LSW theory must be modified to describe real systems. The new theory provides a comprehensive approach to understanding microstructural coarsening in two-phase systems.