Telomeric DNA progressively erodes with each round of cell division in cells that do not express telomerase, a specialized reverse transcriptase necessary to fully duplicate the chromosomal ends. Telomerase is expressed in tumor cells but not in most somatic cells and thus telomeres and telomerase may be proposed as attractive targets for the discovery of new anticancer agents. In this paper we will present different strategies to inhibit telomerase activity via an interaction with a telomere/telomerase nucleic acid component, with a special emphasis on quadruplex ligands.