Recent years have witnessed an ever growing interest in theoretically studying chemical processes at surfaces. Apart from the interest in catalysis, electrochemistry, hydrogen economy, green chemistry, atmospheric and interstellar chemistry, theoretical understanding of the molecule-surface chemical bonding and of the microscopic dynamics of adsorption and reaction of adsorbates are of fundamental importance for modeling known processes, understanding new experimental data, predicting new phenomena, controlling reaction pathways. In this work, we review the efforts we have made in the last few years in this exciting field. We first consider the energetics and the structural properties of some adsorbates on metal surfaces, as deduced by converged, first-principles, plane-wave calculations within the slab-supercell approach. These studies comprise water adsorption on Ru(0001), a subject of very intense debate in the past few years, and oxygen adsorption on aluminum, the prototypical example of metal passivation. Next, we address dynamical processes at surfaces with classical and quantum methods. Here the main interest is in hydrogen dynamics on metallic and semi-metallic surfaces, because of its importance for hydrogen storage and interstellar chem- istry. Hydrogen sticking is studied with classical and quasi-classical means, with particular emphasis on the relaxation of hot-atoms following dissociative chemisorption. Hot atoms dynamics on metal surfaces is investigated in the reverse, hydrogen recombination process and compared to Eley-Rideal dynamics. Finally, Eley-Rideal, collision-induced desorption, and adsorbate-induced trapping are studied quantum mechanically on a graphite surface, and unexpected quantum effects are observed.