Eukaryotic cells, from yeast to mammals, respond and adapt to environmental and microenvironmental stressors by evolutionary conserved multicomponent endogenous systems that utilise a network of signal transduction pathways to regulate the adaptive and protective phenotype. The balance between cell survival and cell death is decisive for sensitivity or resistance to DNA-damaging chemotherapeutic agents. Anticancer drugs may themselves act as stressors to induce adaptive signals that could limit their clinical value. Related research has been focused on the modulation of the expression and function of the heat shock proteins, the unfolded protein response, the mechanisms of subcellular translocation of signalling components, the genomic and non-genomic actions of drugs and endogenous functional components like hormonal pathways, the input of inflammation and alterations in the microenvironmental milieu and on the control of the cell cycle and proliferation. The outcome seems to be driven by the first-line responses that support cellular integrity and by specific mechanisms that depend on the type of cell and the nature, and duration and severity of the noxious stimulus. Data obtained from experimental organisms like the yeast have added valuable information on the basic conservation in cellular stress-related processes in eukaryotes and on the consequences that may accompany the adaptive and protective phenotype during the stress response to anticancer agents. Understanding the complex molecular pathways mediating these processes has started to contribute to the reevaluation of the current therapeutic regiments and to revolutionise the approaches for improved anticancer therapy.