In the first part of the talk, the behavior of weakly bound clusters exposed to XUV radiation in two different regimes of intensity is discussed. At the intensities provided by third-generation synchrotron radiation sources, only one-photon absorption plays a role. A cluster is singly ionized and a hole in the valence shell is formed. In atoms and small molecules, an inner valence hole is electronically stable, but in clusters an ultrafast, Auger-like decay process can occur. This process, referred to as Interatomic Coulombic Decay (ICD), is characterized by an efficient Coulombic energy transfer mechanism between monomers in the cluster. The talk provides a basic overview of the phenomenon of ICD. The most important theoretical predictions are presented, together with recent experimental evidence for ICD in neon clusters. Then, motivated by a recent experiment using the new free-electron laser at DESY in Hamburg (Germany), the interaction of xenon clusters with intense VUV radiation is analyzed. In the experiment, xenon clusters were found to absorb a very large number of VUV photons. The theoretical description developed accounts for the experimental observation. Key aspects are the rapid formation of a dense nanoplasma and the efficiency of photon absorption in electron-ion collisions, a process known as Inverse Bremsstrahlung.

The second part of the talk focuses on nonlinear optical processes in atoms. The Hamburg free-electron laser is sufficiently intense to allow for the production of multiply charged ions in a gas of atomic xenon. The multiphoton ionization of xenon and its ions is discussed within a Floquet-based theoretical framework, taking into account the temporal structure of the individual VUV laser pulses. Challenges for experiments with future x-ray free-electron lasers are pointed out. The talk closes with a description of a joint experimental and theoretical project that develops the methodology for future pump-probe experiments using x-ray free-electron lasers. A versatile technique is reported for probing isolated atom response and also collective ion dynamics within the strong-field environment created by a focused laser using micro-focused, tunable, pulsed hard x-rays. Further, the polarization of the x-ray microprobe is exploited to probe directly the alignment of the residual ion core created in tunnel ionization.