Growing recognition of the numerous, diverse and important roles played by non-coding RNA in all organisms motivates better elucidation of these cellular components. Comparative genomics is a powerful tool for this task and is arguably preferable to any high-throughput experimental technology currently available, because evolutionary conservation highlights functionally important regions. Conserved secondary structure, rather than primary sequence, is the hallmark of many functionally important RNAs, because compensatory substitutions in base-paired regions preserve structure. Unfortunately, such substitutions also obscure sequence identity and confound alignment algorithms, which complicates analysis greatly. This paper surveys recent computational advances in this difficult arena, which have enabled genome-scale prediction of cross-species conserved RNA elements. These predictions suggest that a wealth of these elements indeed exist