Aptamers are short single-stranded nucleic acid molecules with a unique ability to bind with high specificity andaffinity to a wide range of biomolecules, including proteins, viruses, and small molecules, due to the formation of tertiary structures, making them a powerful alternative to antibodies in biosensing, diagnostics, and therapy. Their advantages, such as high stability, the possibility of targeted chemical modification, and reproducible solid-phase synthesis without the use of cell-based systems or bioreactors, have driven the active development of methods for their design and optimization. This review systematizes the key stages in the evolution of aptamer development technologies, starting with the classic SELEX technology, and considers its modifications, including CE-SELEX, M-SELEX, Cell-SELEX, HT-SELEX, and others, aimed at improving the efficiency, specificity, and automation of the process. Special attention is paid to the integration of computational methods such as secondary and tertiary structure prediction (RNAfold, MXfold2, RNAComposer), molecular docking (AutoDock Vina, HADDOCK, ZDOCK), molecular dynamics (GROMACS, AMBER, NAMD), and SELEX data analysis (AptaSUITE, FASTAptamer). The implementation of machine learning and deep learning algorithms (AptaDiff, RaptGen, Apta-MCTS, Xelari) is also described, opening up new opportunities for the rational design of de novo aptamers, optimization of their affinity, and minimization of experimental costs. The review discusses the limitations of the current methods, such as limited amount of structural data, the complexity of predicting noncanonical pairs and pseudoknots, and the insufficient generalizability of ML models to new sequence families. This review highlights the transformative potential of aptamers in biomedicine but emphasizes the need for rigorous experimental validation of computational predictions to overcome current limitations.