Some historical documents, especially the Einstein-Besso manuscript from 1913, an extensive notebook by Hans Thirring from 1917, and a correspondence between Thirring and Albert Einstein in the year 1917 reveal that most of the merit of the so-called Lense-Thirring effect of general relativity belongs to Einstein. Besides this ``central story" of the effect, we comment shortly on some type of prehistory, with contributions by Mach, Benedikt and Immanuel Friedlaender, and August Foeppl, and we follow the later history of the problem of a correct centrifugal force inside a rotating mass shell which was resolved only relatively recently. We also shortly comment on recent possibilities to confirm the so-called Lense-Thirring effect, and the related Schiff effect, experimentally.