Extreme weather events and climate change are two of the main threats for society of the 21st century. Extreme weather events caused over 500 thousand casualties and over 2 trillion USD economic damages in the past 20 years. A failure of climate change mitigation and adaptation targets is ranked among the leading threats to global society. At the 2015 Paris Climate Conference, leaders from 194 countries of the world unanimously acknowledged the serious threat posed by anthropogenic emissions of greenhouse gases. Society must now become resilient to changes in climate over coming decades, which requires making quantitative estimates for future changes of weather patterns and climate extremes. This includes exceptional weather events such as violent windstorms and flash floods, but also persistent anomalies in planetary-scale circulation patterns, which lead to pervasive flooding in some regions and seasons, and long-lived drought and extremes of heat in others. Numerical models of the Earth system represent the most important tool to anticipate and assess these kinds of threats. One of the main factors that is limiting the skill of these models is limited resolution, and resolution, in turn, is limited by computational power that can be leveraged by these models. The first two phases of the ESiWACE Centre of Excellence (COE) have pushed the resolution of global Earth system models to unprecedented levels. This includes the first global atmosphere models that were able to run at ~1 km resolution in the first phase of ESiWACE and coupled atmosphere/ocean models that were able to