The higher order structure of an RNA is often essential to its biological function, modulating its interactions with ligands, protein partners, and other RNAs. Modeling RNA secondary structure, assessing the accuracy of RNA structural models, and discovering new functional motifs are challenging problems that are confounded by the length and complexity of the studied RNA. Improvements in structure modeling accuracy can be made by incorporating SHAPE (selective 2'-hydroxyl acylation analyzed by primer extension) and DMS (dimethyl sulfate) chemical probing data, however these models remain imperfect. In this work I apply principals of molecular modeling in interpret chemical probing experiments and create analytical and experimental tools that enable large-scale experiment-driven modeling of RNA interactions and structures. First, I use electronic structure modeling to propose a mechanism to explain the preferential reactivity of the SHAPE reagent 1M6 at nucleotides exhibiting an available open stack in folded RNAs. I also use molecular modeling at the nucleotide level to develop a model that accurately predicts the disruptive effects of SHAPE adducts on RNA tertiary structure. Second, I create a new energy potential for RNA structure prediction using information from a three-reagent SHAPE experiment that increases the accuracy of modeling accuracy from 85% to above 90% for some of the most difficult-to-predict RNA structures. Third, working collaboratively with others in the lab, I validate a new approach for melding SHAPE chemical probing with deep sequencing in a new technique termed SHAPE mutational profiling (SHAPE-MaP). The ability to quickly generate structural data for RNAs of unprecedented size using SHAPE-MaP presents a new challenge: accurately modeling large RNA secondary structures. To solve this problem I develop software, called SuperFold, which uses a windowed modeling algorithm to enable rapid secondary structure prediction and discovery of the most stable structural motifs in long RNAs. Fourth, I extend the RING-MaP experiment and analysis to enable use with random primers and applied it to the bacterial ribosome. With the improved RING-MaP experiment I am able to detect structural interaction networks within the small ribosomal subunit. Additionally, I am able to perturb those structural networks by adding the antibiotic spectinomycin. Coupled together, the work presented here will provide valuable tools that democratize RNA structure analysis and help others in the RNA community understand the role of RNA structure at new and exciting scales.