ABSTRACT The Mediterranean basin is a hot spot of climate change in simulated scenarios, where effects are already observable. Increases in some climate extremes (terrestrial and marine heatwaves, agricultural droughts, extreme precipitation in some areas, and fire weather) are already observed. These extremes are expected to further increase in the future, together with more frequent pluvial and coastal floods, a reduction in cyclone and medicanes frequency (but increase of their maximum intensity) and increasing meteorological droughts. This review paper addresses methodological advances in the science of extreme event attribution, that is, techniques to better understand how much anthropogenic climate change affected the intensity, frequency and physical processes leading to observed extreme weather events, with a focus on studies in the Mediterranean basin.