Complete collapse of the West Antarctic Ice Sheet (WAIS) would raise global sea level by around 5 m, but whether collapse is likely, or even possible, has been `glaciology’s grand unsolved problem’ for more than two decades. Collapse of WAIS may result from readjustments continuing since the last glacial maximum, or more recent climate change, but it is also possible that collapse will result from internal flow instabilities, or not occur at all in the present inter-glacial. Such complexity led the Intergovernmental Panel on Climate Change to conclude in its Second Assessment Report that `estimating the likelihood of a collapse during the next century is not yet possible’. However, a refusal by scientists to estimate the risk leaves policy-makers with no sound scientific basis on which to respond to legitimate public concerns. Here we present a discussion of the likelihood of WAIS-collapse, drawing input from an interdisciplinary panel of experts. The results help to summarise the state of scientific knowledge and uncertainty. While the overall opinion of the panel was that WAIS most likely will not collapse in the next few centuries, their uncertainty retains a 5% probability of WAIS causing sea level rise at least 10 mm/year within 200 years. Since this uncertainty reflects both the unpredictability of the physical system and the scientific uncertainty, it will undoubtedly change as a better understanding is established.