Cells have evolved to dynamically respond to different types of environmental and physiological stress conditions. The information about a previous stress stimulus experience by a mother cell can be passed to its descendants, allowing them to better adapt to and survive in new environments. In recent years, live-cell imaging combined with cell-lineage tracking approaches has elucidated many important principles that guide stress inheritance at the single-cell and population level. In this review, we summarize different strategies cells can employ to pass the ‘memory’ of previous stress responses to their descendants. Among these strategies, we focus on a recent discovery of how specific features of Msn2 nucleo-cytoplasmic shuttling dynamics could be inherited across cell lineages. We also discuss how stress response can be transmitted to progenies through changes in chromatin and through partitioning of anti-stress factors and/or damaged macromolecules between mother and daughter cells during cell division. Finally, we highlight how emergent technologies will help address open questions in the field.