After reviewing some elementary properties of RNA, we discuss how statistical mechanics can be used to determine the secondary structure of RNA. The idea is to first parametrize (as well as possible) the free energy of secondary structures. Given such a parametrization, we review the algorithms used for the prediction of secondary structures without pseudoknots. To include pseudoknots, we propose a classification of RNA structures in terms of their topological genii. This classification is based on matrix field-theories. We modify the free energy parametrization so as to include a penalty proportional to the genus of the RNA structure, and we show how with this new parametrization, one can efficiently predict RNA structures with pseudoknots.