We theoretically studied the reversible adsorption of polymers onto selected rigid and soft chemically non-uniform adsorbing surfaces with an emphasis on the polymer adsorption onto the selective binary mixed brushes. In the course of our study, we developed two independent theoretical methods, the self-consistent perturbation expansion and the transfer operator formalism, which made it possible to thoroughly investigate the density structure of polymers adsorbed onto chemically non-uniform substrates. As successive stages of our research, we applied the above theoretical methods to the polymer adsorption onto the selected substrates, as follows: (i) periodically patterned rigid surface; (ii) randomly patterned rigid surface; (iii) surface that bears an array of periodically distributed adsorption centers; (iv) different morphologies of the mixed brush. By comparing the results for the above listed systems we derived the qualitative trends that are common for the polymer adsorption onto the investigated chemically non-uniform substrates. The obtained information has been used to investigate the polymer adsorption onto different morphologies of the selective binary mixed brush. In particular, we calculated the surface excesses of polymers adsorbed onto the two different morphologies (`ripple' and random) of the binary mixed brush. In addition, the developed theory has been used to study the polymer adsorption onto the non-uniform binary brush in the presence of the gradient of chemical composition. The interplay between the depletion effect caused by the loss of the polymer entropy in the interior of the brush and attractive interaction between the adsorbed polymer and surface of the brush is shown to lead to a reach adsorption-desorption behavior that is described by the developed theory. The obtained results are presented in the form of adsorption-desorption diagrams that are calculated for different values of the degree of polymerisation, Flory-Huggins interaction parameters, and the grafting density of the brush. The calculated surface excesses has been proven to critically depend on the relation between the radius of gyration of adsorbed polymer and characteristic size of the surface pattern. It is shown that regular patterned brush surface is more efficient in adsorbing shorter (relative to the size of the pattern) polymers, as compared to the random brush surface. The effect of the excluded volume is found to reduce the adsorption of polymers onto the mixed brush and lead to the suppression of the polymer localization within the selective brush species.