Free-Electron Lasers in the extreme ultraviolet and in the X-ray regime offer ultrashort photon pulses with extremely high peak brilliance. These properties open exiting new possibilities for research in laser-matter interactions, ultrafast science, spectroscopy, and structural analysis with applications in physics, chemistry, materials science, and life sciences. The novel sources will allow to probe matter on atomic length and time scales with unprecedented detail. Fascinating science is envisioned in the fields of femtosecond dynamics of non-equilibrium states and ultrafast processes in molecules, clusters and condensed matter systems as well as in life sciences. This will be complemented by novel imaging techniques based on the unique coherence properties of the new sources. In my talk I will report on first scientific results obtained in the XUV-regime with the Free-Electron Laser in Hamburg (FLASH) in operation since 2005. In addition, I will review the status and the perspectives of the European X-ray Free-Electron Laser facility (XFEL) to be built at DESY in Hamburg.