At the surface of a solid, quantum mechanics allows the existence of two-dimensional Bloch waves as solutions of the Schrödinger equation. These "surface" states are interesting both for fundamental and practical reasons, and have been extensively explored, e.g., on pure metals. Conversely, relatively few studies exist of the electronic states of artificially-grown two-dimensional structures. This work is an investigation, mainly by angle-resolved photoemission, of different heterogeneous surfaces of defined stoichiometry, formed by a large-Z p metal on a noble metal substrate, which constitute what is called a "surface alloy". A breakthrough has been obtained on the Bi/Ag(111) (√3 × √3)R30° structure, which presents a band dispersion split into two spin polarized replicas in momentum space by the spin-orbit coupling. The effect is known as Rashba-Bychkov splitting in semiconductors, and it is a genuine effect of the symmetry breaking occurring at the surface, but in Bi/Ag(111) it is much larger than reported in any other compound. This sets this class of materials among the suitable candidates for spintronics applications, which have been object of rising interest in the last years. We have put our attention on other surface alloys, varying substrates (Ag(111) and Cu(111)) and adsorbates (Bi, Pb, Sb) in order to set the basis for a unifying description of the quantities involved in the determination of the size of the splitting, and in particular to discriminate between atomic and structural contributions. An analogous band structure is found in all the systems, consisting namely of two "sets" of bands with negative effective mass, originating from the hybridization between the surface states of the substrate and the p electrons of the adsorbate. We have identified a significant in-plane component of the electric potential gradient, which is not present in pure metal surfaces, as the new element most likely responsible for the large size of the splitting. At the same time, the results show that a necessary condition for it to be effective in enhancing the splitting is a strong atomic spin-orbit parameter. Our findings are confirmed by first-principle calculations, which reproduce quantitatively the band structure, and by a nearly free electron model, which qualitatively supports our interpretation of the role of the in-plane gradient. A parallel project of this thesis has concerned Yb-based Kondo systems, as studied by hard x-ray photoemission and inelastic x-ray scattering. At these high energies, photoemission probes a thicker region below the sample surface, where heavy-fermion compounds stabilize in a different electronic configuration with respect to that of the bulk. We have shown that the temperature dependence of the 4f spectral function is in line with the predictions of the Anderson impurity model, a point which has often been questioned on the basis of previous results of low-energy photoemission. On the other hand, by a comparison with inelastic scattering, we have noticed that the latter leads to a better agreement with the data from thermodynamic and transport measurements. We conclude that, despite the unique capability of photoemission of accessing directly the electron spectral function, photon-in–photon-out spectroscopies are a more trustworthy probe of the bulk electronic structure.