Insufficient internet access is holding back local economies, reducing educational outcomes, and creating health disparities in rural areas of the U.S. At present, federal and state funding is available for rural broadband infrastructure deployment, but existing efforts have not invested in analytical work to maximize efficiency and minimize cost. In this study, we use a state-of-the-art matrix (SAM) to identify key challenges and opportunities facing rural broadband infrastructure from previous research and government reports. We focus on six themes: (1) technology, (2) hardware costs, (3) financing, (4) adoption, (5) regulatory/legal, and (6) management. We highlight key issues to be addressed by both private and public decision-makers to effectively manage broadband investment as well as engage stakeholders to improve access and adoption. Much of the challenge for rural broadband infrastructure is related to a low return on investment due to high capital costs and low population densities. However, there are many innovative approaches to overcoming this barrier from technical, policy, and social perspectives. Unfortunately, adoption and management are understudied and would benefit from additional research to design effective decision-making tools and programs. From a systems perspective, solutions that leverage tools from a diverse set of perspectives, rather than purely focusing on technology deployment, are more likely to be sustainable in the long-term. We outline an agenda for future work based on the needs of rural communities as well as local and state governments.