The selective delivery of drugs in a cell- or tissue-specific manner represents the main challenge for medical research; in order to reduce the occurrence of unwanted off-target effects. In this regard, nucleic acid aptamers have emerged as an attractive class of carrier molecules due to their ability to bind with high affinity to specific ligands; their high chemical flexibility; as well as tissue penetration capability. To date, different aptamer-drug systems and aptamer–nanoparticles systems, in which nanoparticles function together with aptamers for the targeted delivery, have been successfully developed for a wide range of therapeutics, including toxins; peptides; chemotherapeutics and oligonucleotides. Therefore, aptamer-mediated drug delivery represents a powerful tool for the safe and effective treatment of different human pathologies, including cancer; neurological diseases; immunological diseases and so on. In this review, we will summarize recent progress in the field of aptamer-mediated drug delivery and we will discuss the advantages, the achieved objectives and the challenges to be still addressed in the near future, in order to improve the effectiveness of therapies.