Coreference and many forms of ellipsis are similar to reading comprehension questions, in that in order to resolve these, we need to identify an appropriate text span in the previous discourse. This paper exploits this analogy and proposes to use an architecture developed for machine comprehension for ellipsis and coreference resolution. We present both single-task and joint models and evaluate them across standard benchmarks, outperforming the current state of the art for ellipsis by up to 48.5% error reduction -- and for coreference by 37.5% error reduction.