Recent studies demonstrating the existence of special noncoding "antisense" RNAs used in post transcriptional gene regulation have received considerable attention. These RNAs are synthesized naturally to control gene expression in C. elegans, Drosophila, and other organisms; they are known to regulate plasmid copy numbers in E. coli as well. Small RNAs have also been artificially constructed to knock out genes of interest in humans and other organisms for the purpose of finding out more about their functions. Although there are a number of algorithms for predicting the secondary structure of a single RNA molecule, no such algorithm exists for reliably predicting the joint secondary structure of two interacting RNA molecules or measuring the stability of such a joint structure. In this paper, we describe the RNA-RNA interaction prediction (RIP) problem between an antisense RNA and its target mRNA and develop efficient algorithms to solve it. Our algorithms minimize the joint free energy between the two RNA molecules under a number of energy models with growing complexity. Because the computational resources needed by our most accurate approach is prohibitive for long RNA molecules, we also describe how to speed up our techniques through a number of heuristic approaches while experimentally maintaining the original accuracy. Equipped with this fast approach, we apply our method to discover targets for any given antisense RNA in the associated genome sequence.