This article describes the discovery of X-rays by William Conrad Röntgen. That work, which earned Röntgen the first Nobel Prize in Physics, was one of the initial contributions to the new field of nuclear physics. Röntgen's experiments and reactions to his work are described in detail. He was concerned at first that the images of the bones he had X-rayed were somehow connected with spiritualism. Previous work by William Crookes and Philipp Lenard, which laid the foundation for Röntgen's studies, is also described, as well as how other scientists missed the evidence pointing to the existence of a new type of ray. The article includes some of the first X-ray photographs.