After reviewing some elementary properties of RNA, we discuss how statistical mechanics can be used to determine the secondary structure of RNA. First, one has to parametrize as precisely as possible the free energy of secondary structures. Given such a parametrization, we review some methods used to predict secondary structures without pseudoknots. To include pseudoknots, we propose a classification of RNA structures in terms of their topological genii. This topological classification stems from a matrix field- theory representation of the RNA folding problem. The free energy is parametrized so as to include a penalty proportional to the genus of the RNA structure. We present an algorithm based on these ideas to efficiently predict RNA structures with pseudoknots.