In this work, a selection of unresolved topics regarding the electronic and atomic structures of Si and Ge surfaces, both clean ones and those modified by metal adsorbates, are addressed. The results presented have been obtained using theoretical calculations and experimental techniques such as photoelectron spectroscopy (PES), low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). Si(001) surfaces with adsorbed alkali metals can function as prototype systems for studying properties of the technologically important family of metal-semiconductor interfaces. In this work, the effect of up to one monolayer (ML) of Li on the Si(001) surface is studied using a combination of experimental and theoretical techniques. Several models for the surface atomic structures have been suggested for 0.5 and 1 ML of Li in the literature. Through the combination of experiment and theory, critical differences in the surface electronic structures between the different atomic models are identified and used to determine the most likely model for a certain Li coverage. In the literature, there are reports of an electronic structure at elevated temperature, that can be probed using angle resolved PES (ARPES), on the clean Ge(001) and Si(001) surfaces. The structure is quite unusual in the sense that it appears at an energy position above the Fermi level. Using results from a combined variable temperature ARPES and LEED study, the origin of this structure is determined. Various explanations for the structure that are available in the literature are discussed. It is found that all but thermal occupation of an ordinarily empty surface state band are inconsistent with our experimental data. In a combined theoretical and experimental study, the surface core-level shifts on clean Si(001) and Ge(001) in the c(4×2) reconstruction are investigated. In the case of the Ge 3d core-level, no previous theoretical results from the c(4×2) reconstruction are available in the literature. The unique calculated Ge 3d surface core-level shifts facilitate the identification of the atomic origins of the components in the PES data. Positive assignments can be made for seven of the eight inequivalent groups of atoms in the four topmost layers in the Ge case. Furthermore, a similar, detailed, assignment of the atomic origins of the shifts on the Si surface is presented that goes beyond previously published results. At a Sn coverage of slightly more than one ML, a 2√3 × 2√3 reconstruction can be obtained on the Si(111) surface. Two aspects of this surface are explored and presented in this work. First, theoretically derived results obtained from an atomic model in the literature are tested against new ARPES and STM data. It is concluded that the model needs to be revised in order to better explain the experimental observations. The second part is focused on the abrupt and reversible transition to a molten 1×1 phase at a temperature of about 463 K. ARPES and STM results obtained slightly below and slightly above the transition temperature reveal that the surface band structure, as well as the atomic structure, changes drastically at the transition. Six surface states are resolved on the surface at low temperature. Above the transition, the photoemission spectra are, on the other hand, dominated by a single strong surface state band. It shows a dispersion similar to that of a calculated surface band associated with the Sn-Si bond on a 1×1 surface with Sn positioned above the top layer Si atoms. There has been extensive studies of the reconstructions on Si surfaces induced by adsorption of the group III metals Al, Ga and In. Recently, this has been expanded to Tl, i.e., the heaviest element in that group. Tl is different from the other elements in group III since it exhibits a peculiar behavior of the 6s2 electrons called the “inert pair effect”. This could lead to a valence state of either 1+ or 3+. In this work, core-level PES is utilized to find that, at coverages up to one ML, Tl exhibits a 1+ valence state on Si(111), in contrast to the 3+ valence state of the other group III metals. Accordingly, the surface band structure of the 1/3 ML √3 x √3 reconstruction is found to be different in the case of Tl, compared to the other group III metals. The observations of a 1+ valence state are consistent with ARPES results from the Si(001):Tl surface at one ML. There, six surface state bands are seen. Through comparisons with a calculated surface band structure, four of those can be identified. The two remaining bands are very similar to those observed on the clean Si(001) surface.