The fresh water export from the Arctic has not been measured yet. The major problem lies in the transport over the shallow East Greenland shelf that is not easily accessible for oceanographic vessels and so far has been off-limits for moored instrumentation. Even if we would be able to start measurements now, we would have no statistics to evaluate trends and natural variability of the transport. For long time series and for predictions of future changes, there is no other means than numerical models of the oceanic circulation and the water mass distribution. For past times, models can perhaps be combined with observations of different variables to yield better reconstructions of long-term variability in fresh water fluxes between the Arctic and the sub-polar North Atlantic. © 2008 Springer Netherlands.