No existing algorithm can start with arbitrary RNA sequences and return the precise, three-dimensional structures that ensures their biological function. This chapter outlines current algorithms for automated RNA structure prediction (including our own FARNA-FARFAR), highlights their successes, and dissects their limitations, using a tetraloop and the sarcin/ricin motif as examples. The barriers to future advances are considered in light of three particular challenges: improving computational sampling, reducing reliance on experimentally solved structures, and avoiding coarse-grained representations of atomic-level interactions. To help meet these challenges and better understand the current state of the field, we propose an ongoing community-wide CASP-style experiment for evaluating the performance of current structure prediction algorithms.