Aptamers are short single-stranded DNA, RNA, or synthetic Xeno nucleic acids (XNA) molecules that can interact with corresponding targets with high affinity. Owing to their unique features, including low cost of production, easy chemical modification, high thermal stability, reproducibility, as well as low levels of immunogenicity and toxicity, aptamers can be used as an alternative to antibodies in diagnostics and therapeutics. Systematic evolution of ligands by exponential enrichment (SELEX), an experimental approach for aptamer screening, allows the selection and identification of in vitro aptamers with high affinity and specificity. However, the SELEX process is time consuming and characterization of the representative aptamer candidates from SELEX is rather laborious. Artificial intelligence (AI) could help to rapidly identify the potential aptamer candidates from a vast number of sequences. This review discusses the advancements of AI pipelines/methods, including structure-based and machine/deep learning-based methods, for predicting the binding ability of aptamers to targets. Structure-based methods are the most used in computer-aided drug design. For this part, we review the secondary and tertiary structure prediction methods for aptamers, molecular docking, as well as molecular dynamic simulation methods for aptamer–target binding. We also performed analysis to compare the accuracy of different secondary and tertiary structure prediction methods for aptamers. On the other hand, advanced machine-/deep-learning models have witnessed successes in predicting the binding abilities between targets and ligands in drug discovery and thus potentially offer a robust and accurate approach to predict the binding between aptamers and targets. The research utilizing machine-/deep-learning techniques for prediction of aptamer–target binding is limited currently. Therefore, perspectives for models, algorithms, and implementation strategies of machine/deep learning-based methods are discussed. This review could facilitate the development and application of high-throughput and less laborious in silico methods in aptamer selection and characterization.