Restructuring-type adsorption, in which substrate surface atoms are replaced, migrate and are rearranged, of alkali-metal atoms on low index surfaces of fcc metals is reviewed. In such adsorption the restructuring occurs at room or slightly higher temperatures, whereas overlayers are formed at lower temperatures. We classify eight composite surface-structures formed by the restructuring-type adsorption. Detailed structures and condition for the formation of each structure are described. In addition we include similar composite surface-structures formed by metal adsorption other than alkali-metals.