The impact of melt ponds on Arctic sea ice is estimated from model simulations of the historical and future climate. The simulations were performed with and without the effect of melt ponds on sea ice melt, respectively. In the last thirty years of the historical simulations, melt ponds develop predominantly in the continental shelf regions and in the Canadian archipelago. Accordingly, the ice albedo in these regions is systematically smaller than in the no-pond simulations, the sea ice melt is enhanced, and both the ice concentration and ice thickness during the September minimum are reduced. Open ponds decrease the ice albedo, resulting in enhanced ice melt, less sea ice and further pond growth. This positive feedback entails a more realistic representation of the seasonal cycle of Northern Hemisphere sea ice area. Under the premise that the observed decline of Arctic sea ice over the period of modern satellite observations is mainly externally driven and, therefore, potentially predictable, both model versions underestimate the decline in Arctic sea ice. This presupposition, however, is challenged by our model simulations which show a distinct modulation of the downward Arctic sea ice trends by multidecadal variability. At longer time scales, an impact of pond activation on Arctic sea ice trends is more evident: In the Representative Concentration Pathway scenario RCP45, the September sea ice is projected to vanish by the end of the 21st century. In the active-pond simulation, this happens up to two decades earlier than in the no-pond simulations.