This thesis outlines the development of several methods for improving RNA secondary and tertiary structure prediction. Novel non-coding RNAs (ncRNAs) are discovered to play various roles in living organisms. A profound understanding of their structures is crucial for learning their functional mechanisms. In Chapter 2, a statistical RNA energy scoring function was developed based on a distance-scaled finite ideal-gas reference state (DFIRE_RNA). The energy score is tested by discriminating native and near-native structures from other decoy structures. We showed that this energy function has a higher success rate in detecting native and near-native structures than other energy functions. In Chapter 3, RNAcmap was established to perform RNA contact prediction based on homology search and evolutional covariance analysis. RNAcmap extended the applicability of evolution-based contact prediction from RNAs within manually curated RNA families to all RNAs. This method has the performance in contact prediction comparable to those generated from the default Rfam alignment. In Chapter 4, RNAmrf was developed to construct multiple sequence alignment based on the probabilistic graph theory. This method for the first time is able to account for pseudoknot base-pairing in sequence alignment that was ignored by existing covariance models. The new method was demonstrated to improve over existing methods in aligning sequences with pseudoknots as well as prediction of pseudoknot base pairs. These tools are available at https://sparks-lab.org/ and should facilitate the tasks of predicting RNA secondary and tertiary structures.