Understanding how RNAs interact with proteins, RNAs, or other molecules remains a challenge of main interest in biology, given the importance of these complexes in both normal and pathological cellular processes. Since experimental datasets are starting to be available for hundreds of functional interactions between RNAs and other biomolecules, several machine learning and deep learning algorithms have been proposed for predicting RNA-RNA or RNA-protein interactions. However, most of these approaches were evaluated on a single dataset, making performance comparisons difficult. With this review, we aim to summarize recent computational methods, developed in this broad research area, highlighting feature encoding and machine learning strategies adopted. Given the magnitude of the effect that dataset size and quality have on performance, we explored the characteristics of these datasets. Additionally, we discuss multiple approaches to generate datasets of negative examples for training. Finally, we describe the best-performing methods to predict interactions between proteins and specific classes of RNA molecules, such as circular RNAs (circRNAs) and long non-coding RNAs (lncRNAs), and methods to predict RNA-RNA or RNA-RBP interactions independently of the RNA type.