The adsorption of a Cs atom on planar (C6H6 and C24H12) and nonplanar (C20H10 and C21H9) carbon clusters has been studied using the density-functional theory, with the local-density approximation and atomic pseudopotentials. Binding energies as a function of separation have been calculated for several configurations of the Cs atom on the different substrates. The adsorption on sites above the center of carbon rings is more stable than adsorption on top of carbon atoms and C-C bonds. In the case of the curved clusters, adsorption on the concave side is preferred compared to the convex side. The Cs bonding is stronger on the nonplanar clusters. The strength of the binding energy depends on two effects: the magnitude of the highest occupied molecular orbital-lowest unoccupied molecular orbital (LUMO) energy gap of the substrate, and the energy of the valence state of Cs relative to the LUMO of the substrate. Due to a favorable relative position of those two energy levels, charge transfer occurs from Cs to the two nonplanar clusters, and this provides an ionic contribution to the bonding. The analysis of the electronic density redistribution and of the local Fukui functions helps in the interpretation of the charge transfer and the reactivity.