The interaction of hydrogen with palladium surfaces represents a model system for the study of the adsorption and absorption at metal surfaces. Theoretical gas-surface dynamics studies have usually concentrated on the adsorption dynamics on clean surfaces. Only recently has it become possible, based on advances in electronic structure codes and improvements in computer power, to address the much more complex problem of the adsorption dynamics on precovered surfaces. Herein, recent ab initio molecular dynamics studies are discussed that address the adsorption dynamics of hydrogen molecules on hydrogen- and sulfur-precovered Pd surfaces. In addition, the relaxation dynamics of the hydrogen atoms after the dissociation on clean Pd(100) are presented.