The discovery of the Röntgen rays and the events connected to it are extraordinary in many respects. Röntgen never disclosed the full details of the experiment which led to the discovery on November 8, 1895. He observed the x-rays by chance. Neither he nor any other scientist had an idea that such radiation might exist. However, it needed a Röntgen to make the discovery, an experimenter of his superior capabilities. His achievement was the culmination point of the development of physics as an experimental science in the 19th Century. This development of physics is described in this report in some detail, together with the institutional structure of university physics in Germany and the status of technical achievements at the time of Röntgen. Röntgen was suspicious, if not disdainful, of theoretical physics which slowly had gained in importance and in institutional representation. Thus, Röntgen's famous discovery, possible only to a mind not prejudiced by theoretical considerations or expectations, happened at a point in the history of physics when predominantly theoretical concepts introduced the paradigm change from "classical" to "modern" physics: Maxwell's electromagnetic theory, Planck's quantum hypothesis, and Einstein's relativity principle and explanation of the photo-electric effect. The tremendous speed by which the news of the "new kind of rays" spread around the world and the sensation this news caused launched an intensity of research on x-rays unprecedented in other areas of research and is reflected in a description of the publication history. The traditional working style of the Institute Director Röntgen, the structure of his Institute, his lack of interest in theory, the burden of his sudden fame and other factors made it practically impossible for him to compete with the rapid development and to contribute substantially to the research on x-rays. Even the award of the first Nobel Prize in physics in 1901 did not stimulate him to undertake new research activities. He even succeeded in avoiding presentation of his Nobel Lecture. He took the role of the interested observer, sometimes diverted by priority disputes, mainly with Lenard, or by sensational press reports, and retreated increasingly into final solitude, possibly his answer also to the abundance of honors heaped upon him. The impact of his discovery was, however, enormous. In physics it gave impulses to the discovery of radioactivity, of the identification of the electron, and the development of the model of the atom; and in medicine in its immediate applications in diagnosis and therapy.