Surface carbides of cobalt and nickel are exceptionally stable, having stabilities competitive with those of graphitic C on these surfaces. The unusual structure of these carbides has attracted much attention: C assumes a tetracoordinate square-planar arrangement, in-plane with the metal surface, and its binding favors a spontaneous p4g clock surface reconstruction. A chemical bonding model for these systems is presented and explains the unusual structure, special stability, and the reconstruction. C promotes local two-dimensional aromaticity on the surface and the aromatic arrangement is so powerful that the required number of electrons is taken from the void M4 squares, thus leading to Peierls instability. Moreover, this model predicts a series of new transition-metal and main-group-element surface alloys: carbides, borides, and nitrides, which feature high stability, square-planar coordination, aromaticity, and a predictable degree of surface reconstruction.