In this talk, we'll describe two steps forward in meeting this challenge. The first contribution is a new set of thermodynamic parameters, which improve the accuracy of MFE structure prediction. We use optimization and machine learning methods to infer our parameters from a large repository of known structures, as well as from thermodynamic data obtained experimentally. Secondly, we will describe new combinatorial algorithms for MFE pseudoknotted structure prediction, which are more efficient than previous algorithms for certain types of pseudoknotted structures. We will also discuss possible directions for further improvements in secondary structure prediction.