Progress in the theoretical understanding of catalysis by size-selected subnanometer (or ultranano) metal clusters deposited onto an oxide surface is reviewed. Attention is focused on a few simple general concepts that can help orienting oneself in this rapidly developing but already extensive field: (i) the fluxional character of ultrananoclusters and the associated need for systematically sampling the system's potential energy surface; (ii) the influence of the underlying support (including possible defects) in terms of epitaxial relationships, generated electrostatic field and electronic interactions, and the possible active role of the support in the reaction mechanisms; (iii) the evolution of ligand adsorption energetics, structure and dynamics as a function of coverage, including many-body and synergic interactions among ligands, and the formation of catalytically active species; (iv) the robustness of the catalyst in terms of surface diffusion and cluster disaggregation. The possibility of out-of-equilibrium effects and the theoretical methodology required for their predictive description are also briefly mentioned. These concepts are illustrated via selected examples drawn from our own recent work.