An aptamer is a single-stranded DNA or RNA that binds to a specific target with high binding affinity. Aptamers are developed through the process of systematic evolution of ligands by exponential enrichment (SELEX), which is repeated to increase the binding power and specificity. However, the SELEX process is time-consuming, and the characterization of aptamer candidates selected through it requires additional effort. Here, we describe in silico methods in order to suggest the most efficient way to develop aptamers and minimize the laborious effort required to screen and optimise aptamers. We investigated several methods for the estimation of aptamer-target molecule binding through conformational structure prediction, molecular docking, and molecular dynamic simulation. In addition, examples of machine learning and deep learning technologies used to predict the binding of targets and ligands in the development of new drugs are introduced. This review will be helpful in the development and application of in silico aptamer screening and characterization.