A scaling theory is developed for selective adsorption of polymers induced by the strong binding between Specific monomers old complementary surface adsorption sites. By "selective" we mean specific attraction between a subset of all monomers, called "sticky", and a subset of surface sites, called "adsorption sites". We demonstrate that, in addition to the expected dependence on the polymer volume fraction phi(bulk) it the bulk solution, selective adsorption strongly depends on the ratio between two characteristic length scales, the root-mean-square distance I, between neighboring sticky monomers along the polymer, and the average distance d between neighboring surface adsorption Sites. The role of the ratio lid arises from the fact that a polymer needs to. deform to enable the spatial commensurability between its sticky monomers and the surface adsorption sites for selective adsorption. We study strong selective adsorption of both telechelic polymers with two end monomers being sticky and multisticker polymers with many sticky monomers between sticky ends. For telechelic polymers, we identify four adsorption regimes at l/d < 1 that are characterized by the fraction of occupied adsorption Sites and whether the dominant conformation of adsorbed chains is a single-end-adsorbed "mushroom" or double-end-adsorbed loop. For l/d > 1, we expect that the adsorption layer at exponentially low phi(bulk) consists of separated unstretched loops, while as phi(bulk), increases the layer crosses over to a brush of extended loops with a second layer of weakly overlapping tails. For multisticker chains, in the limit of exponentially low phi(bulk), adsorbed polymers are well separated from each other. As lid increases,the conformation of an individual polymer changes from a single-end-adsorbed "mushroom" to a random walk of loops. For high phi(bulk), adsorbed polymers at small l/d are mushrooms that cover all the adsorption sites. At sufficiently large l/d, adsorbed multisticker polymers Strongly overlap. We anticipate the formation of a self-similar carpet and with increasing l/d a two-layer structure with a brush of loops covered by a self-similar carpet. As l/d exceeds the threshold determined by the adsorption energy, the brush of loops under the carpet reaches a saturated state, resulting in a lid-independent brush-under-carpet structure, which can also be applied to describe adsorbed rnultisticker polymers in nonselective adsorption where a sticker can strongly bind to any place on the adsorption surface. We examine the adsorbed amount Gamma of multisticker polymers in different regimes for selective adsorption. If the adsorbed multisticker polymers are nonoverlapping mushrooms, the adsorbed amount Gamma increases linearly with the surface density of adsorption sites Sigma approximate to 1/d(2) In the self-similar carpet regime, Gamma increases sublinearly as vas. in a good solvent, while only logarithmically in a theta solvent. Formation of a brush layer under the carpet contributes an additional adsorbed amount. This additional amount increases linearly with Sigma and eventually dominates the overall adsorbed amount Gamma before saturating at a plateau value controlled by the adsorption energy.