First experiments on atomic photoionization and molecular dissociation have been performed by taking advantage of the unprecedented characteristics of the free electron laser in Hamburg (FLASH) combined with a separate near-infrared (NIR) femtosecond laser. In a series of two-colour experiments, the photoionization of rare gases in the presence of a strong NIR dressing field as well as the polarization dependence of this process were investigated systematically. A detailed analysis of the partial cross sections for the two-colour two-photon ionization process was carried out for low dressing fields. Higher dressing fields gave rise to multi-photon processes, which were observed and analysed without undesirable interferences, a beneficial consequence of the monochromaticity of the FLASH radiation. The experimental results were compared with theoretical descriptions for two-colour above-threshold ionization obtained by employing second-order perturbation theory and the ‘soft-photon’ approximation. In addition, complementary information was obtained on the sequential two-photon double ionization of Ne, which was made possible by the short and intense FLASH pulses. As a starting point for future time-resolved studies of molecular dissociation, a proof-of-principle experiment on the hydrogen diatomic system was carried out. In a typical pump–probe arrangement, excited neutral fragments, which were formed during photo-induced dissociation by the FLASH radiation, were identified via single- and multi-photon ionization induced by the time-delayed optical laser.