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Protein-RNA interactions are of vital importance to a variety of cellular activities. Both experimental and computational techniques have been developed to study the interactions. Due to the limitation of the previous database, especially the lack of protein structure data, most of the existing computational methods rely heavily on the sequence data, with only a small portion of the methods utilizing the structural information. Recently, AlphaFold has revolutionized the entire protein and biology field. Foreseeably, the protein-RNA interaction prediction will also be promoted significantly in the upcoming years. In this work, we give a thorough review of this field, surveying both the binding site and binding preference prediction problems and covering the commonly used datasets, features, and models. We also point out the potential challenges and opportunities in this field. This survey summarizes the development of the RBP-RNA interaction field in the past and foresees its future development in the post-AlphaFold era.