In this talk, I share a vision of interactive research papers, where user interfaces surface information for readers when and where they need it. Grounded in tools that I and my collaborators have developed, I discuss what it takes to design reading interfaces that (1) surface definitions of terms where readers need them (2) explain the meaning of math notation and (3) convey the meaning of jargon-dense passages in simpler terms. In our research, we have found that effective reading support requires not only sufficient document processing techniques, but also the careful presentation of derived information atop visually complex documents. I discuss tensions and solutions in designing interactive papers, and identify future research directions that can bring about powerful augmenting reading experiences.