This paper presents a theoretical basis for the design of e-Proofs , electronic resources to support proof comprehension in undergraduate mathematics. To begin, we frame the problems of teaching for proof comprehension, giving research background and an argument about what teacher-centred lecturing does not, and cannot, do to address these. We then describe e-Proofs, discuss the way in which they have been used in an Analysis course, and review their limitations and affordances as part of an overall educational experience. Finally, we briefly describe the development of a web-based tool for constructing e-Proofs, ways in which this tool will be used to different pedagogical ends, and associated research activity.