Atoms are the smallest building blocks of matter, and their behavior and their particular arrangement in larger systems such as molecules, clusters, nanoparticles and solids define many properties of these larger entities. The investigation of isolated, multi-electron atoms therefore highlights the fundamental aspects of light-matter interaction. Free-electron laser sources offer unique possibilities to study the interaction of atoms and intense radiation in the VUV, XUV and X-ray wavelength regimes. Due to the high irradiance levels produced by these ultra-bright sources, various non-linear processes, such as multi-photon ionization, above threshold ionization and sequential multiple ionization, can be explored at these photon energies. Moreover, the short pulse duration allows insight into the dynamics of electronic relaxation through the additional interaction with an overlapping synchronized optical laser. Special emphasis is placed on fundamental multi-photon processes as well as on applications of atomic photoionization for the characterization of the temporal properties of free-electron laser pulses.