[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI--COLUMBIA AT REQUEST OF AUTHOR.] RNA (Ribonucleic acid) molecules play a variety of crucial roles in cellular functions at the level of transcription, translation and gene regulation. RNA functions are often tied to its 3D structure and dynamics. To quantitatively understand the relationship between RNA functions and its 3D structures and kinetics, we need a computational model for RNA folding. My research involves several components about theoretical and computational modeling of RNA folding. To provide a user friendly tool for RNA biologists, we developed a fully-automated web interface and software for RNA 2D and 3D structure prediction from nucleotide sequence. The software and webserver is based on the Vfold2D and Vfold3D models developed by our lab. A key issue in the current RNA structure prediction methods is modeling of loop structures. In Vfold2D model, we use a physics-based coarse-grained representation for RNA conformations which samples all the possible loop conformations in 3D space to calculate the loop entropy and free energy parameters. For the 3D structure prediction, we use a template-based method to assemble RNA 3D structures from motifs. In a cell, an RNA folds as it is transcribed and the process is kinetically controlled. To predict RNA folding kinetics in a cell, based on a helix-based rate model, we developed a new method for sampling cotranscriptional RNA conformation ensemble and prediction of cotranscriptional folding kinetics. Applications to E. Coli. SRP RNA and pbuE riboswitch indicate that the model may provide reliable predictions for the cotranscriptional folding pathways and population kinetics. For E. Coli. SRP RNA, the predicted population kinetics and the folding pathway are consistent with those from profiles in the recent cotranscriptional SHAPE-seq experiments. For the pbuE riboswitch, the model predicts the transcriptional termination efficiency as a function of the force. The theoretical results show (a) a force-induced transition from the aptamer (antiterminator) to the terminator structure and (b) the different folding pathways for the riboswitch with and without the ligand (adenine). More Specifically, without adenine, the aptamer structure emerges as a short-lived kinetic transient state instead of a thermodynamically stable intermediate state. Furthermore, from the predicted extension-time curves, the model identifies a series of conformational switches in the pulling process, where the predicted relative residence times for the different structures are in accordance with the experimental data. The model may provide a new tool for quantitative predictions of cotranscriptional folding kinetics and results can offer useful insights into cotranscriptional folding-related RNA functions such as regulation of gene expression with riboswitches. One of the major roadblocks for RNA structure prediction is the effects of ion concentrations and loop sequence. However, most structure prediction models do not explicitly consider ion and loop sequence effects. RNA hairpin is one the most fundamental motifs in RNA structures. To predict the ion and loop sequence effects, we developed a novel integrated computational approach by combining 2D and 3D folding models with an ion electrostatic model. We demonstrate that the approach not only predicts folding stabilities that quantitatively agree with experiment results but also provides detailed structural and energetic insights into the hairpin stability. The approach developed here is general and can be directly applied to treat general RNA systems.