Nucleic acid aptamers represent a class of single-stranded oligonucleotides capable of high-affinity and specific binding to diverse targets, including proteins, small molecules, cells, and metal ions. Their advantages over antibodies—such as simpler synthesis, lower immunogenicity, superior stability, and easier modification—have positioned them as powerful tools in therapeutics, diagnostics, and biosensing. This review systematically surveys the integral role of bioinformatics and artificial intelligence (AI) in modern aptamer development, spanning from in silico selection and structural prediction to the generative design of novel aptamer sequences. The application of high-throughput SELEX (HT-SELEX) has greatly accelerated the discovery of aptamers, but also introduced computational challenges in processing large-scale sequencing data. Bioinformatics pipelines now routinely include tools like AptaPLEX and AptaSuite for preprocessing raw reads, including demultiplexing, adapter trimming, and quality filtering. Subsequent analytical steps involve clustering-based tools (e.g., FASTAptamer, AptaCLUSTER) to identify enriched sequences, and motif discovery algorithms (such as AptaTRACE and MPBind) that uncover conserved sequence-structure patterns associated with binding functionality. These approaches allow researchers to move beyond manual curation and extract meaningful candidates from complex selection rounds. Accurate prediction of secondary and tertiary structures is essential for understanding aptamer function and interaction mechanisms. Conventional tools, including RNAfold and Mfold, employ thermodynamics-based models to predict RNA folding, yet often struggle with pseudoknots and non-canonical pairs. Recent advances in deep learning—exemplified by SPOT-RNA, E2Efold, and UFold—have significantly improved prediction accuracy by leveraging neural networks trained on large structural datasets. For tertiary structure, methods range from fragment assembly (Rosetta FARFAR2) and homology modeling (RNAComposer) to deep learning-aided approaches such as AlphaFold-RNA and RoseTTAFoldNA. While these tools offer new insights, predicting structures for short, flexible aptamers remains non-trivial. Predicting aptamer–target interactions draws on both physics-based and data-driven approaches. Molecular docking programs—AutoDock Vina, ZDOCK, and MDockPP—provide initial binding poses, which can be refined using molecular dynamics simulations (with GROMACS, AMBER, or NAMD) and free energy perturbation techniques to estimate binding affinity. Complementarily, machine learning models are increasingly employed to predict interactions from sequence and structural features. Early efforts used hand-engineered features with classifiers like SVM and random forest, while contemporary deep learning models (AptaNet, AptaBERT, PAIR) utilize pre-trained language models to capture intricate sequence-binding relationships with superior generalization. Perhaps the most transformative development is the use of generative AI for de novo aptamer design. Conditional variational autoencoders (e.g., RaptGen), generative adversarial networks (e.g., AptaDesigner), and diffusion models (e.g., AptaDiff) can generate novel aptamer sequences conditioned on target properties or desired binding affinities. Reinforcement learning and evolutionary algorithms, including Monte Carlo tree search (Apta-MCTS) and NSGA-II, support multi-objective optimization toward high specificity, stability, and low immunogenicity. These approaches mark a paradigm shift from selective discovery to intentional design, greatly expanding the functional sequence space. Aptamers designed via these computational strategies are increasingly applied in biomedical and environmental fields, including as targeted therapeutics, diagnostic biosensors, and agents in food safety monitoring. Nonetheless, key challenges persist: data scarcity and heterogeneity, model interpretability, and experimental validation bottlenecks. Future progress will depend on standardized data sharing, improved explainable AI, and the integration of computational design with high-throughput experimental screening—ultimately enabling robust, clinically viable aptamer technologies.