The article discusses the results of simulation-based and experimental research carried out on gas foil bearings. Owing to the use of a set of flexible thin foils in such bearings, they exhibit certain beneficial features that cannot be found in other types of bearings. They have nonlinear operational characteristics and allow the dissipation of excess energy, thus reducing the vibration level. Moreover, gas foil bearings can self-adapt themselves to the current operating conditions by changing the shape of the lubrication gap. Therefore, they can be used to improve the dynamic performance of rotors, in particular, those operating at very high rotational speeds. This article explains the mechanisms for changes of stiffness and vibration damping in compliant components of a foil bearing. The results of the analysis of the bearing’s subassemblies using advanced numerical models are presented. They are followed by conclusions that were drawn not only from these results but also from the results of the experimental research. It has been proven that the rotor supported on carefully designed foil bearings is capable of maintaining a low vibration level, even if it operates at a high rotational speed.