Recent findings show that coding genes are not the only targets that miRNAs interact with. In fact, there is a pool of different RNAs competing with each other to attract miRNAs for interactions, thus acting as competing endogenous RNAs (ceRNAs). The ceRNAs indirectly regulate each other via the titration mechanism, i.e. the increasing concentration of a ceRNA will decrease the number of miRNAs that are available for interacting with other targets. The cross-talks between ceRNAs, i.e. their interactions mediated by miRNAs, have been identified as the drivers in many disease conditions, including cancers. In recent years, some computational methods have emerged for identifying ceRNA-ceRNA interactions. However, there remain great challenges and opportunities for developing computational methods to provide new insights into ceRNA regulatory mechanisms. In this paper, we review the publically available databases of ceRNA-ceRNA interactions and the computational methods for identifying ceRNA-ceRNA interactions (also known as miRNA sponge interactions). We also conduct a comparison study of the methods with a breast cancer dataset. Our aim is to provide a current snapshot of the advances of the computational methods in identifying miRNA sponge interactions and to discuss the remaining challenges.