Research with cold molecules has developed rapidly in recent years. There is now a variety of established methods for cooling molecules into the millikelvin range. Nevertheless, a focal point of current research is directed toward finding new ways to bring the temperature of molecules even closer to absolute zero. Samples of cold molecules offer not only important applications for high-resolution spectroscopy, which benefit from the increased interaction time of slow molecules with electromagnetic radiation; they also promise access to an exotic regime of chemical reactivity, in which phenomena such as quantum tunneling and quantum resonances predominate. This review begins with an introduction to the methods by which cold molecules can be prepared, with special emphasis on Stark deceleration and traps. In addition to applications of cold molecules that have already been partially achieved, an important focus of the review concentrates on possible future applications, and both aspects are illustrated with selected examples.