MicroRNAs form one of the groups of small noncoding RNA molecules that have completely changed our understanding of gene regulatory networks. Because microRNAs have been discovered only relatively recently, most of their functions remain unknown, providing a challenge to both experiment and theory. I review several computational approaches pursued in our group to answer this challenge. In particular, I show that a few rather simple ideas can go a long way in predicting accurately genes regulated by microRNAs via binding sites both in the coding and 3' untranslated regions (3'UTRs). Finally, I mention briefly several applications, including two collaborations with experimental groups, which have shed new light on the latency and reactivation of herpesviruses, and on the maturation of red blood cells.