Long non-coding RNAs (lncRNAs) and microRNAs (miRNAs) are two prevalent non-coding RNAs in current research. They play critical regulatory roles in the life processes of animals and plants. Studies have shown that lncRNAs can interact with miRNAs to participate in post-transcriptional regulatory processes, mainly involved in regulating cancer development, metastatic progression, and drug resistance. Additionally, these interactions have significant effects on plant growth, development, and responses to biotic and abiotic stresses. Deciphering the potential relationships between lncRNAs and miRNAs may provide new insights into our understanding of the biological functions of lncRNAs and miRNAs, and the pathogenesis of complex diseases. In contrast, gathering information on lncRNA-miRNA interactions (LMIs) through biological experiments is expensive and time-consuming. With the accumulation of multi-omics data, computational models are extremely attractive in systematically exploring potential LMIs. To the best of our knowledge, this is the first comprehensive review of computational methods for identifying LMIs. Specifically, we first summarized the available public databases for predicting animal and plant LMIs. Second, we comprehensively reviewed the computational methods for predicting LMIs and classified them into two categories, including network-based methods and sequence-based methods. Third, we analyzed the standard evaluation methods and metrics used in LMI prediction. Finally, we pointed out some problems in the current study and discuss future research directions. Relevant databases and the latest advances in LMI prediction are summarized in a GitHub repository https://github.com/sheng-n/lncRNA-miRNA-interaction-methods, and we'll keep it updated.