Anthropogenic impacts have perturbed the planet to the edge of the known “safe operating space” for human civilization, and it is now practically certain that global climate will overshoot the “safe” temperature limits of the Paris Agreement. In this unprecedented future, there is a growing risk of crossing tipping points into a new, and potentially irreversible, state. This Voices asks, where are the thresholds, and the potential broader impacts, of crossing tipping points in an overshoot world?