This volume of the Series Grapholinguistics gathers contributions by the participants of the Graphemics in the 21st Century (/gʁafematik/) conference that was organized by Yannis Haralambous with the support of IMT Atlantique and the CNRS (UMR 6285 LabSTICC, unit DECIDE) and was held in Brest from June 13 to June 15, 2018.Its aim was to bring together disciplines concerned with writing sys tems and their representation in written communication, as well as to reflect on the current state of research in the area, and on the role that writing and writing systems play in neighboring disciplines like com puter science and information technology, communication, typography, psychology, and pedagogy.Not surprisingly, the papers gathered in this volume belong to var ious disciplines and consider writing from different points of view, in volving linguistics, history, archeology, education, and natural language processing.In his paper " 'Alphabetic writing is in and for itself the more intel ligent Form'. Reflections on the evaluation of writing systems" (in Ger man language), Coulmas takes Hegel's statement in favor of the alpha betic script as a starting point and questions whether, and how, writ ing systems can be compared. This paper is followed by Küster's "Open and Closed Writing Systems. Some Reflections," which gives a differ ent classification approach of scripts based on their openness, e.g., their possibility to increase their set of graphs.The paper "The History of the Graphematic Foot in English and Ger man" by Evertz deals with a notion inspired by the phonological foot unit (hierarchically located between the syllable and the word), the gra phematic foot. The author discusses its pertinence, providing examples in English and German.In several languages there have been attempts to provide genderneu tral forms. The paper "Graphemic Methods for GenderNeutral Writing" by Haralambous & Dichy describes a particular case of genderneutral forms, namely graphemic ones, in