Over the past decade, evidence from disciplines ranging from biology to economics has suggested that many scientific studies may not be reproducible. This has led to declarations in both the scientific and lay press that science is experiencing a "reproducibility crisis" and that this crisis has consequences for the extent to which students, faculty, and the public at large can trust research. Faculty build on these results with their own research, and students and the public use these results for everything from patient care to public policy. To build a model for how academic libraries can support reproducible research, the authors conducted a review of major guidelines from funders, publishers, and professional societies. Specific recommendations were extracted from guidelines and compared with existing academic library services and librarian expertise. The authors believe this review shows that many of the recommendations for improving reproducibility are core areas of academic librarianship, including data management, scholarly communication, and methodological support for systematic reviews and data-intensive research. By increasing our knowledge of disciplinary, journal, funder, and society perspectives on reproducibility, and reframing existing librarian expertise and services, academic librarians will be well positioned to be leaders in supporting reproducible research.