In the course of digitisation, the range of substrates for textual reading is being expanded to include a number of screen-based technologies and reading devices, such as e-readers (e.g. Kindle) and tablets (e.g. iPad). These technologies have distinctly different affordances than paper has. Given that textual reading is at the same time likely to remain important as a cultural practice, and is undergoing massive change as digital screens are supplementing paper--with the potential to replace it as the dominant substrate--there is an urgent need to investigate what effects such change might have on the reading of different kinds of texts, for different purposes. This article proposes the need for an integrative, transdisciplinary model of embodied, textual reading accounting for its psychological, ergonomic, technological, social, cultural and evolutionary aspects. The envisaged model aims to be partly explanatory, in the sense that it aligns and integrates existing knowledge, and partly exploratory, in the sense that it points to blank spots in our knowledge where further research is needed. The model will thus serve to guide the planning of such further research, and to make research more compatible and research outcomes more widely useable.