Brownian aggregation in concentrated hard-sphere dispersions is studied using models and Brownian dynamics (BD) simulations. Two new theoretical models are presented and compared to several existing approaches and BD simulation results, which serve as benchmarks. The first new model is an improvement over an existing local density approximation (LDA)-based model. The other is based on the more rigorous Fundamental measure theory (FMT) applied to the "liquid-state" dynamic density-functional theory (DDFT). Both models provide significant improvements over the classical Smoluchowski model. The predictions of the new FM-DDFT-based model for aggregation kinetics are in excellent agreement with BD simulation results for dispersions with initial particle volume fractions, phi, up to 0.35 (close to the hard-sphere freezing transition at phi = 0.494). In contrast to previous approaches, the nonideal particle diffusion effects and the initial and time-dependent short-range ordering in concentrated dispersions due to entropic packing effects are explicitly considered here, in addition to the unsteady-state effects. The greater accuracy of the FM-DDFT-based model compared to that of the LDA-based models indicates that nonlocal contributions to particle diffusion (only accounted for in the former) play important roles in aggregation. At high concentrations, the FM-DDFT-based model predicts aggregation half-times and gelation times that are up to 2 orders of magnitude shorter than those of the Smoluchowski model. Moreover, the FMDDFT-based model predicts asymmetric cluster-cluster aggregation rate constants, at least for short times. Overall, a rigorous mechanistic understanding of the enhancement of aggregation kinetics in concentrated dispersions is provided.