Tipping points in the climate system are thresholds where a tiny change could push the system into a completely new state. They are of particular interest in reference to concerns about global warming. The EU-funded CriticalEarth project will train 15 early-stage researchers on new methods for assessing the mechanisms and associated risks of critical transitions in the climate. The focus will be on investigating how complex mathematics can be used to predict and avoid irreversible climate change. The network will offer researchers an excellent background for working with cross-disciplinary teams in academia, industry, and governmental and non-governmental institutions.