Interactions between RNAs and proteins play essential roles in many important biological processes. Benefitting from the advances of next generation sequencing technologies, hundreds of RNA-binding proteins (RBP) and their associated RNAs have been revealed, which enables the large-scale prediction of RNA-protein interactions using machine learning methods. Till now, a wide range of computational tools and pipelines have been developed, including deep learning models, which have achieved remarkable performance on the identification of RNA-protein binding affinities and sites. In this review, we provide an overview of the successful implementation of various deep learning approaches for predicting RNA-protein interactions, mainly focusing on the prediction of RNA-protein interaction pairs and RBP-binding sites on RNAs. Furthermore, we discuss the advantages and disadvantages of these approaches, and highlight future perspectives on how to design better deep learning models. Finally, we suggest some promising future directions of computational tasks in the study of RNA-protein interactions, especially the interactions between noncoding RNAs and proteins. This article is categorized under: RNA Interactions with Proteins and Other Molecules > Protein-RNA Interactions: Functional Implications RNA Evolution and Genomics > Computational Analyses of RNA RNA Interactions with Proteins and Other Molecules > Protein-RNA Recognition.