Short wavelength Free-Electron Lasers (FELs) are among the newest light sources available to scientists to probe a wide range of phenomena, with chemical, physical and biological applications, using soft and hard X-rays. These sources include the currently most powerful hard X-ray light sources in the world and are characterized by extremely high powers and high transverse coherence, but the first FELs had, and many still have, reduced longitudinal coherence. Now it is possible to achieve good longitudinal coherence (narrow bandwidth in the frequency domain) and here we discuss and illustrate a range of experiments utilizing this property, and their underlying physics. The primary applications are those which require high resolution (for example resonant experiments), or temporal coherence (for example coherent control experiments). The currently available light sources extend the vast range of laboratory laser techniques to short wavelengths.