Despite tremendous interest in the topic and decades of research, the origins of the major losses of biodiversity in the history of life on Earth remain elusive. A variety of possible causes for these mass-extinction events have been investigated, including impacts of asteroids or comets, large-scale volcanic eruptions, effects from changes in the distribution of continents caused by plate tectonics, and biological factors, to name but a few. Many of these suggested drivers involve or indeed require changes of Earth's climate, which then affect the biosphere of our planet, causing a global reduction in the diversity of biological species. It can be argued, therefore, that a detailed understanding of these climatic variations and their effects on ecosystems are prerequisites for a solution to the enigma of biological extinctions. Apart from investigations of the paleoclimate data of the time periods of mass extinctions, climate-modelling experiments should be able to shed some light on these dramatic events. Somewhat surprisingly, however, only a few comprehensive modelling studies of the climate changes associated with extinction events have been undertaken. These studies will be reviewed in this paper. Furthermore, the role of modelling in extinction research in general and suggestions for future research are discussed.