Noncoding RNAs (ncRNAs) play prominent roles in the regulation of gene expression via their interactions with other biological molecules such as proteins and nucleic acids. Although much of our knowledge about how these ncRNAs operate in different biological processes has been obtained from experimental findings, computational biology can also clearly substantially boost this knowledge by suggesting possible novel interactions of these ncRNAs with other molecules. Computational predictions are thus used as an alternative source of new insights through a process of mutual enrichment because the information obtained through experiments continuously feeds through into computational methods. The results of these predictions in turn shed light on possible interactions that are subsequently validated experimentally. This review describes the latest advances in databases, bioinformatic tools, and new in silico strategies that allow the establishment or prediction of biological interactions of ncRNAs, particularly miRNAs and lncRNAs. The ncRNA species described in this work have a special emphasis on those found in humans, but information on ncRNA of other species is also included.