A significant barrier to effective cancer therapy is the development of resistance to the drugs utilised. Standard chemotherapeutic regimens typically contain genotoxic agents, designed to damage DNA of existing tumour cells as well as prevent the synthesis of new DNA during proliferation. DNA damage in normal cells can be repaired efficiently or tolerated to preserve cellular and organ functionality. The mechanisms of DNA repair and tolerance are distinct for different types of lesion, but can be predicted if the mechanism of interaction of the drug with the DNA is known. There is now evidence in solid tumours to suggest that increased repair or tolerance of DNA lesions may contribute to the ability of the cancer cell to survive in high genotoxic stress environments afforded by the therapy. This review will explore the current understanding of drug resistance mechanisms to chemotherapy, but will focus on the new evidence for tolerance and repair, including some new data from the authors' laboratory on the haematological malignancy multiple myeloma. The review will focus particularly on the role of the 'specialised polymerases' which have flexible active sites capable of accommodating DNA lesions, allowing replication past the lesion by translesion synthesis and tolerance of the damage, which ultimately results in a phenotype of drug resistance.