Certain guanine-rich (G-rich) DNA and RNA molecules can associate intermolecularly or intramolecularly to form four stranded or "quadruplex" structures, which have unusual biophysical and biological properties. Several synthetic G-rich quadruplex-forming oligodeoxynucleotides have recently been investigated as therapeutic agents for various human diseases. We refer to these biologically active G-rich oligonucleotides as aptamers because their activities arise from binding to protein targets via shape-specific recognition (analogous to antibody-antigen binding). As therapeutic agents, the G-rich aptamers may have some advantages over monoclonal antibodies and other oligonucleotide-based approaches. For example, quadruplex oligonucleotides are non-immunogenic, heat stable and they have increased resistance to serum nucleases and enhanced cellular uptake compared to unstructured sequences. In this review, we describe the characteristics and activities of G-rich oligonucleotides. We also give a personal perspective on the discovery and development of AS1411, an antiproliferative G-rich phosphodiester oligonucleotide that is currently being tested as an anticancer agent in Phase II clinical trials. This molecule functions as an aptamer to nucleolin, a multifunctional protein that is highly expressed by cancer cells, both intracellularly and on the cell surface. Thus, the serendipitous discovery of the G-rich oligonucleotides also led to the identification of nucleolin as a new molecular target for cancer therapy.