Free-electron X-ray lasers driven by linear accelerators open exciting new research opportunities in physics, chemistry, material- and geo-sciences as well as in structural biology. After a description of the principle of a free-electron laser, the results obtained at the FEL at the TESLA Test Facility at DESY will be presented. Saturation has been achieved at 98 nm and first experiments on ablation and free clusters have been performed. In 2004 a user facility will be available for wavelengths down to 24 nm and later down to 6 nm. Together with a linear collider for particle physics, a free-electron X-ray laser laboratory has been presented in March 2001 as part of the TESLA project. The layout of the laser facility and aspects of its scientific case will be presented.