Chemotherapy is intended to induce cancer cell death through apoptosis and other avenues. Unfortunately, as discussed in this article, moderate doses of genotoxic drugs such as cisplatin typical of those achieved in the clinic often invoke a cytostatic/dormancy rather than cytotoxic/apoptosis response in solid tumour-derived cell lines. This is commonly manifested by an extended apoptotic threshold, with extensive apoptosis only being seen after very high/supralethal doses of such agents. The dormancy response can be associated with senescence-like features, polyploidy and/or multinucleation, depending in part on the p53 status of the cells. In most solid tumour-derived cells, dormancy represents a long-term survival mechanism, ultimately contributing to disease recurrence. This review highlights the nonlinearity of key aspects of the molecular and cellular responses to bulky DNA lesions in human cells treated with chemotherapeutic drugs (e.g., cisplatin) or ultraviolet light-C (a widely used tool for unraveling details of the DNA damage-response) as a function of the level of genotoxic stress. Such data highlight the growing realization that targeting dormant cancer cells, which frequently emerge following conventional anticancer treatments, may represent a novel strategy to prevent or, at least, significantly suppress cancer recurrence.