Interpreting the tsunami of sequence information for RNA would be facilitated by an understanding of all the physical principles determining RNA structure. In principle, a complete understanding would make it computationally possible to find RNA sequences that fold for function and to predict their three-dimensional structure. It would, thus, also facilitate discovery of new principles relating structure to function. This review covers some of the progress in understanding RNA over roughly the preceding 40 years and suggests progress still to be made. © 2013 Wiley Periodicals, Inc. Biopolymers 99: 1097–1104, 2013.