The polypeptide chains that make up proteins have thousands of atoms and hence millions of possible inter-atomic interactions. It might be supposed that the resulting complexity would make prediction of protein structure and protein-folding mechanisms nearly impossible. But the fundamental physics underlying folding may be much simpler than this complexity would lead us to expect: folding rates and mechanisms appear to be largely determined by the topology of the native (folded) state, and new methods have shown great promise in predicting protein-folding mechanisms and the three-dimensional structures of proteins.