A quarter of all fatalities in the world today is attributed to cancer-related illness. Despite a wide range of anti-cancer drugs being developed over the last sixty years or more, conventional chemotherapies still suffer from major drawbacks, including ineffectiveness and severe side effects, due to a lack of specificity. The emerging field of nanomedicine provides a whole range of materials and techniques for the development of customizable drug delivery vehicles, which can assist the targeting of therapeutic agents to the desired location in the body and thus help to overcome some of the issues. Amongst these, carbon nanotubes (CNTs) have emerged as promising candidates, as they are capable of penetrating mammalian cell membranes and allow for the attachment of high loads of drugs and targeting agents. This thesis investigates the potential of CNTs as a multimodal, targeted delivery system for the anti-cancer drugs doxorubicin and mitoxantrone. To introduce selectivity, a monoclonal antibody and folic acid were tested as active targeting agents. It was first shown that the drug delivery system is effectively taken up by cancer cells with subsequent intracellular release of the anti-cancer drug, which then translocates to the nucleus, while the nanotubes remain in the cytoplasm. Next, it was demonstrated that the efficacy of delivery is influenced by the dispersion stability of the functionalized, drug-loaded CNTs, which in turn is controlled by a large number of physical and biological parameters. To optimize the dispersion stability, different surface functionalization schemes were tested and it was found that covalent conjugation of amine-terminated PEG rendered stable CNT dispersions in various media and also reduced deleterious effects on cultured cells. Based on this knowledge, the initially developed drug delivery system was improved and it was shown in an in vitro cancer cell line model that the efficacy of the improved system exceeds that of the free drugs at low drug doses. The attachment of folic acid to the nanotubes, a widely-used active targeting approach, further enhanced the efficacy of the system. Overall, this allows for the administration of lower drug doses and leads to improved safety due to reduced drug-related side effects.