Living organisms are continuously exposed to a myriad of DNA damaging agents that can impact health and modulate disease‐states. However, robust DNA repair and damage‐bypass mechanisms faithfully protect the DNA by either removing or tolerating the damage to ensure an overall survival. Deviations in this fine‐tuning are known to destabilize cellular metabolic homeostasis, as exemplified in diverse cancers where disruption or deregulation of DNA repair pathways results in genome instability. Because routinely used biological, physical and chemical agents impact human health, testing their genotoxicity and regulating their use have become important. In this introductory review, we will delineate mechanisms of DNA damage and the counteracting repair/tolerance pathways to provide insights into the molecular basis of genotoxicity in cells that lays the foundation for subsequent articles in this issue. Environ. Mol. Mutagen. 58:235–263, 2017. © 2017 Wiley Periodicals, Inc.