Extreme climate change, also known as “strange weather,” is anticipated to increase in frequency and magnitude as the effects of anthropogenic climate change amplify over the 21st century. Examples of strange weather include intense downpours, heat waves, and droughts. These increases are driven by the basic physics of the climate system. Extreme climate change will test the resilience of both society and the environment. One of the challenges for the climate community is to advance the mathematical and physical formulation of climate models to provide robust projections of these extreme phenomena. In this talk, we review the state of the science and the prospects for convergent projections of extreme climate change in the limit of ultra-high model resolution.