This special issue gives an overview over the most important topics which are presently debated in the conceptual history. It lays out the challenges faced by the approach and offers suggestions on how to meet them. The introduction proceeds in three steps. First it traces the globalization of the conceptual history and discusses the possibilities for a “Global history of basic concepts.” It then outlines how the conceptual history has moved beyond the thematic field of the Geschichtliche Grundbegriffe, and integrated new topics –in politics and temporality, but also in the natural sciences, and with reference to the body, the senses and emotions–. It finally discusses new methodological challenges, focusing on digital humanities and non-verbal media and sources.