At the end of the summer of 2013, the project ParaTexBib: Paratexts of the Bible: Analysis and Edition of the Greek Textual Transmission, an initiative called into life in 2012 by Martin Wallraff in collaboration with Patrick Andrist, received an Advanced grant from the European Research Council. While the interest of its initiators is to locate, study and publish all paratexts in biblical manuscripts, the ParaTexBib project currently focuses on the approximately 2,300 Greek manuscript witnesses of the Gospels, up to the end of the sixteenth century. As can be imagined, our project raises many theoretical and methodological questions, some of which are briefly outlined here.