Undergraduate mathematics students see a lot of written proofs. But how much do they learn from them? Perhaps not as much as we would like, and perhaps we would like to improve their ability to engage with mathematics by reading. This talk will present a sequence of research studies addressing this issue. It will first describe studies on e-Proofs, which attempted to improve comprehension via proof-specific learning resources. It will then describe an eye-tracking study that provided real-time data on both student and expert mathematical reading. Finally, it will describe the effects of generic mathematical self-explanation training, investigated via both experimental and eye-tracking methods. Together, these studies provide insight into what is special about mathematical reading, and how students can be supported in reading more effectively.