Structured non-coding RNAs play key roles in fundamental cellular processes, but determining their three-dimensional structure remains challenging. In this dissertation, I investigate the feasibility of accurate and consistent de novo modeling of RNA 3D structures at atomic resolution under the Rosetta molecular modeling framework. In the first part, I present a novel RNA structure prediction method called Stepwise Assembly. This method deterministically enumerates a low-energy subspace of the RNA's available conformations through recursively constructing well-packed atomic-detail models in small steps. Stepwise Assembly is shown to systematically outperform existing Monte Carlo and knowledge-based methods for RNA 3D structure prediction. In the second part, I then demonstrate how Rosetta RNA de novo modeling can be combined with non-exchangeable 1H NMR chemical shift data to produce high-resolution RNA structures, without the use of other NMR measurements. The resulting method is rigorously validated on 23 RNA motifs, including 11 blind tests obtained from five leading labs in the RNA NMR community.