Tipping dynamics are triggered when a change in part of the Earth system becomes self-perpetuating beyond a critical threshold (tipping point). This can lead to substantial, widespread, often abrupt and/or irreversible physical, biophysical and/or biogeochemical impacts, which in turn can induce far-reaching socioeconomic impacts. This collection includes papers investigating the risk, likelihood and impacts of crossing tipping points through a variety of approaches and model types, from offline standalone models of individual Earth system components to fully coupled Earth system models. The collection was initiated through TIPMIP, an international initiative that aims to systematically advance our understanding of tipping dynamics in various Earth system components and assess the associated uncertainties.