Fifty years ago, Willi Dansgaard and colleagues discovered several abrupt climate change events in Greenland during the last glacial period. Since then, several ice cores retrieved from the Greenland ice sheet have verified the existence of 25 abrupt climate warming events now known as Dansgaard-Oeschger events. These events are characterized by a rapid 10-15°C warming over a few decades followed by a stable period of centuries or millennia before a gradual return to full glacial conditions. Similar warming events have been identified in other paleo-archives in the Northern hemisphere. These findings triggered wide interest in abrupt climate change and its impact on biological diversity, but ambiguous definitions have constrained our ability to assign biotic responses to the different types of climate change. Here, we provide a coherent definition for different types of climatic change, including 'abrupt climate change', and a summary of past abrupt climate-change events. We then review biotic responses to abrupt climate change, from the genetic to the ecosystem level, and show that abrupt climatic and ecological changes have been instrumental in shaping biodiversity. We also identify open questions, such as what causes species resilience after an abrupt change. However, identifying causal relationships between past climate change and biological responses remains difficult. We need to formalize and unify the definition of abrupt change across disciplines and further investigate past abrupt climate change periods to better anticipate and mitigate the impacts on biodiversity and society wrought by human-made climate change.