Self-assembly of ensembles of supported 2D or 3D nanoclusters (NCs) by surface deposition, and of unsupported 3D NCs by solution-phase synthesis, produces intrinsically nonequilibrium systems. Individual nanoclusters can have far-from-equilibrium shapes and composition profiles. The free energy of the ensemble can be lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening is key for, e.g., avoiding catalyst degradation. In this review, we focus on crystalline metallic NCs. Atomistic-level modeling of equilibration processes typically utilizes stochastic lattice-gas models to access appropriate time-and length-scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution. We also discuss modeling of coarsening including diffusion and decay of individual NCs, and unconventional coarsening processes. We describe high-level modeling integrated with STM studies for 2D epitaxial NCs, and developments in modeling for supported and unsupported 3D NCs motivated by in situ TEM studies.