Nucleic acid sequences containing several short runs of guanine nucleotides can form complex higher order structures, termed quadruplexes. Their occurrence has been most extensively characterised at the telomeric ends of eukaryotic chromosomes, whose DNA comprises such sequences, and where the extreme 3' ends are single-stranded. This enables relatively facile formation of quadruplex arrangements under the influence of a quadruplex-selective small molecule to compete effectively with telomeric protein-DNA interactions. Occurrences of quadruplexes within the human and other genomes have been mapped by bioinformatics surveys, which have revealed over-representations in promoter regions, especially of genes involved in replication, such as oncogenes, as well as in 5'UTR regions. The highly distinctive nature of quadruplex topologies suggests that they can act as novel therapeutic targets, for example in the selective inhibition of transcription of a given oncogene, using designed small molecules to stabilise a particular quadruplex. This offers the prospect of an alternative to, for example, direct kinase targeting with small molecules, without the attendant issues of active-site resistance. We survey here the basis of these approaches, together with current progress, and discuss the mechanistic issues posed by quadruplex targeting.