We describe experimental observations and theoretical analysis of the coarsening of distributions of two-dimensional nanoclusters, either adatom islands or vacancy pits, on metal surfaces. A detailed analyses is provided for Ag(111) and Ag(100) surfaces, although we also discuss corresponding behavior for Cu(111) and Cu(100) surfaces. The dominant kinetic pathway for coarsening can be either Ostwald ripening (OR), i.e., growth of larger clusters at the expense of smaller ones, or Smoluchowski ripening (SR), i.e., diffusion and coalescence of clusters. First, for pristine additive-free surfaces, we elucidate the factors which control the dominant pathway. OR kinetics generally follows the predictions of mesoscale continuum theories. SR kinetics is controlled by the size-dependence of cluster diffusion. However, this size-dependence, together with that of nanostructure shape relaxation upon coalescence, often deviates from mesoscale predictions as a direct consequence of the nanoscale dimension of the clusters. Second, we describe examples for the above systems where trace amounts of a chemical additive lead to dramatic enhancement of coarsening. We focus on the scenario where “facile reaction” of metal and additive atoms leads to the formation of mobile additive-metal complexes which can efficiently transport metal across the surface, i.e., additive-enhanced OR. A suitable reaction-diffusion equation formulation is developed to describe this behavior.