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Adsorbates on metal surfaces have attracted recently the scientific interest both from a fundamental point of view (quantum confinement) and in perspective of application in technology. In particular the electronic properties of such reduced symmetry systems are strictly related to their low dimensionality. An accurate theoretical description of their spectral properties has necessarily to deal with the absence of periodicity that characterizes these systems in one (thin films) or more (adatoms) directions. The embedding method allows to overcome this drawback considering a really infinite system both on vacuum and bulk side. In this thesis the ab initio spectral properties of single adatoms (alkali-metal atom and Ba) on Cu(111) and thin overlayers (K/Cu(111), Bi/Cu(100), O/Fe(100)) are analyzed, also in comparison with experimental results. The capabilities of the theoretical method adopted allow to evidence the role of the substrate band structure on the adsorbates induced electronic states. In particular the aspects related to the resonant charge transfer from the adsorbate's states to the bulk continuum are analyzed. This process represents an elastic decay channel for the surface electronic states and contributes to the elastic lifetime, that we can estimate according to the description of a continuous substrate band structure. The results presented for single adatoms evidence the blockade effect that a surface projected energy gap of the substrate produces on the resonant charge transfer. On the other hand the results relative to the overlayer allows to analyze the complex hybridization mechanism between surface features and substrate states in different points of the surface Brillouin zone. In addition the theoretical description of the electronic properties of overlayers on metal surfaces is devoted in this thesis also to the simulation of experimental findings, namely STM and STS images and photoemission spectra, showing the predictive character of the theoretical approach used.