Plenty of microRNAs (miRNAs) were discovered at a rapid pace in plants, green algae, viruses and animals. As one of the most important components in the cell, miRNAs play a growing important role in various essential and important biological processes. For the recent few decades, amounts of experimental methods and computational models have been designed and implemented to identify novel miRNA-disease associations. In this review, the functions of miRNAs, miRNA-target interactions, miRNA-disease associations and some important publicly available miRNA-related databases were discussed in detail. Specially, considering the important fact that an increasing number of miRNA-disease associations have been experimentally confirmed, we selected five important miRNA-related human diseases and five crucial disease-related miRNAs and provided corresponding introductions. Identifying disease-related miRNAs has become an important goal of biomedical research, which will accelerate the understanding of disease pathogenesis at the molecular level and molecular tools design for disease diagnosis, treatment and prevention. Computational models have become an important means for novel miRNA-disease association identification, which could select the most promising miRNA-disease pairs for experimental validation and significantly reduce the time and cost of the biological experiments. Here, we reviewed 20 state-of-the-art computational models of predicting miRNA-disease associations from different perspectives. Finally, we summarized four important factors for the difficulties of predicting potential disease-related miRNAs, the framework of constructing powerful computational models to predict potential miRNA-disease associations including five feasible and important research schemas, and future directions for further development of computational models.