Guanine-rich repetitive DNA sequences are of particular importance at the ends of chromosomes, where they are associated with a number of proteins to form telomeres. Their function is in large part to protect chromosomal ends from unwanted degradation and chromosomal fusions, although in normal somatic cells telomeres progressively shorten, eventually becoming non-proliferating and consequently these cells have a finite lifetime. By contrast tumour cell telomeres are maintained in length so that tumour cells are effectively immortalised. The reverse transcriptase enzyme telomerase is activated in over 80% of tumour cells, and it undertakes the synthesis of further telomeric DNA repeats, so directly maintaining telomeres. The inhibition of telomerase leads to the senescence and eventual apoptosis of tumour cells, and thus telomerase is an attractive target for selective chemotherapy. This review describes an approach to the inhibition of telomerase that involves the folding of telomeric DNA into a four-stranded quadruplex structure, held together by Hoogsteen hydrogen-bonded arrays of guanine bases. The formation of a quadruplex structure at the 3 end of telomeric DNA effectively hinders telomerase from adding further repeats. A number of small-molecule ligands are described that stabilise quadruplex formation, and which result in telomerase inhibition. Implications for antitumour therapy with such molecules are discussed, and the particular challenges and problems discussed.