Chemotherapeutic agents have been used for the treatment of numerous cancers, but due to poor selectivity and severe systemic side effects, their clinical application is limited. Single-stranded DNA (ssDNA) or RNA aptamers could conjugate with highly toxic chemotherapy drugs, toxins, therapeutic RNAs or other molecules as novel aptamer-drug conjugates (ApDCs), which are capable of significantly improving the therapeutic efficacy and reducing the systemic toxicity of drugs and have great potential in clinics for targeted cancer therapy. In this review, we have comprehensively discussed and summarized the current advances in the screening approaches of aptamers for specific cancer biomarker targeting and development of the aptamer-drug conjugate strategy for targeted drug delivery. Moreover, considering the huge progress in artificial intelligence (AI) for protein and RNA structure predictions, automatic design of aptamers using deep/machine learning techniques could be a powerful approach for rapid and precise construction of biopharmaceutics (i.e., ApDCs) for application in cancer targeted therapy.