During evolution, cells have developed a wide spectrum of stress response modules to ensure homeostasis. The genome and proteome damage response pathways constitute the pillars of this interwoven ‘defensive’ network. Consequently, the deregulation of these pathways correlates with ageing and various pathophysiological states, including cancer. In the present review, we highlight: (1) the structure of the genome and proteome damage response pathways; (2) their functional crosstalk; and (3) the conditions under which they predispose to cancer. Within this context, we emphasize the role of oncogene‐induced DNA damage as a driving force that shapes the cellular landscape for the emergence of the various hallmarks of cancer. We also discuss potential means to exploit key cancer‐related alterations of the genome and proteome damage response pathways in order to develop novel efficient therapeutic modalities. © 2018 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of Pathological Society of Great Britain and Ireland.