The threat of crossing tipping points in the climate system often serves as an argument for more stringent greenhouse gas emission reductions. We introduce such regime shifts into a recursive relative of the DICE integrated assessment model for determining optimal climate policies. Each period's carbon dioxide concentration determines the probability of crossing a tipping point, and the policymaker re-optimizes once a tipping point occurs. The probability, timing, and knowledge of tipping points are endogenous. Our policymaker can also display ambiguity aversion in assessing tipping point uncertainty. We nd that tipping points increase the near-term social cost of carbon by 50-100% when they raise climate sensitivity or make damages more convex. They have less of an eect when they increase the atmospheric lifetime of CO2 or the quantity of non- CO2 greenhouse gases. Uncertainty about tipping points can reduce their eect on policy. The possibility of tipping points is more important for the social cost of carbon than is the ambiguity attitude used in their evaluation.