The ice sheets covering Antarctica and Greenland pose both the largest risk and uncertainty for sea level rise, which is considered to be one of the greatest hazards from future climate change. Together, the two regions contain enough ice to increase sea level by over 60 meters. Predicting the effect of climate change on the ice sheets is challenging because of poorly understood processes and multiple, complex feedbacks among the ice sheets and the rest of the climate system. Policymakers urgently need numbers for future sea level rise and, in particular, an understanding of the uncertainties that come with such predictions. Recently, new initiatives for science-based uncertainty quantification have been launched, revealing mounting concern for ice sheet instability. Panelists at this First Wednesday Seminar characterized the state of the science, methods for quantifying uncertainty, and the potential consequences of abrupt sea level rise.