This thesis comprises work on RNA secondary structure and related graphs. Novel algorithms for predicting RNA secondary structures are presented. These algorithms Incorporate models that had not been used to predict RNA structure before. One model in particular was assumed to have no tractable algorithm. Further, this thesis proposes some new models. The model parameters are tuned through a novel training method, and the results are analysed. Finally, new and faster algorithms for circle graphs, polygon-circle graphs, and interval-filament graphs are presented.