The New Worlds, New Horizons report of the Astro2010 Decadal Survey observed that key challenges in theoretical astrophysics "are of a scale and complexity that require sustained, multi-institutional collaborations," but that there was "no mechanism to support these coordinated efforts at the needed level in the US." NSF's Division of Astronomical Sciences (AST) and NASA's Astrophysics Division (APD) agree that theory and computation are highly complementary "pillars of science," and that major progress in one can enable progress in the other. NSF/AST and NASA/APD have therefore initiated the Theoretical and Computational Astrophysics Networks (TCAN) program with the following goals:To support coordinated efforts in fundamental theory and computational techniques in order to make groundbreaking advances in astrophysics;To strengthen theoretical and computational astrophysics in the US by uniting researchers in collaborative networks that cross institutional and geographical divides; andTo advance the training of the future workforce of theoretical and computational scientists.A network is a combination of nodes and connections. A node is a group of researchers at an existing institution, along with the local resources (e.g., computational, educational, communications) that sustain them. A connection is a significant exchange of expertise or capabilities between nodes (e.g., exchange of personnel, web-based training, sharing of access to resources). Multiple connections between nodes, that enable an integrated and focused collaborative effort, constitute a network. The TCAN program will support research networks with 3 or more nodes at distinct institutions. Proposals must demonstrate clear management structure and clear protocols for communication, planning, distribution of effort, and tracking of progress. Supported projects will develop new theoretical and/or computational paradigms directly addressing key "frontier" questions in astrophysics. In cases where code will be produced for community use, projects will develop a transition plan to maintain and sustain it.TCAN projects are expected to target fundamental issues in theoretical and computational astrophysics and to display a depth and breadth of concept qualitatively beyond those typical of the existing NSF Astronomy and Astrophysics Research Grants (AAG) and NASA Astrophysics Theory Program (ATP) programs. Prospective proposers are strongly urged to contact the cognizant program officers in either or both agencies to discuss the suitability of their projects for the TCAN program before preparing their proposals.