Vibrationally excited adsorbates at surfaces have been suggested to be useful precursors in a number of applications, ranging from spectroscopy over quantum computing, to vibrationally mediated, bond-selective chemistry. To selectively excite adsorbate vibrations, tailored infrared laser pulses can be used, which are, however, perturbed by ultrafast vibrational relaxation. In this talk we shall present approaches of how to calculate vibrational lifetimes, and the laser-driven excitation and quantum dynamics of adsorbates at semiconductor (H/Si(100)) or at metal surfaces (CO/Cu(100) and H/Ru(0001)). For this purpose a reduced description of this system (molecule) / bath (surface) problem is chosen by applying Markovian or non-Markovian open-system density matrix theory, often with relaxation rates determined from perturbation theory. For H/Si, where vibrational relaxation is due to vibration-phonon coupling, in addition a `full' approach is adopted in which a multi-dimensional nuclear Schrödinger equation of the system-bath type is solved by using efficient schemes based on single- or multi-configurational time-dependent Hartree methods.