Icebergs are a significant hazard for polar shipping, and, geophysically, are significant components of the mass balance of continental ice sheets while providing major freshwater inputs to the polar oceans. Some modelling of iceberg trajectories has been undertaken in the past, principally in the Labrador Sea, but here we present a hemispheric-wide attempt to model iceberg motion in the Arctic and North Atlantic Oceans. We show that the basic force balance in iceberg motion is between water drag and water advection, but with the pure geostrophic balance being only a minor component of the latter. Iceberg density maps essentially demonstrate the effect of the major boundary currents but we show that the time and size of calving from individual tidewater glaciers are important variables in determining the ultimate fate of bergs. The biggest bergs never leave the Arctic Ocean. All modelled icebergs have melted after about 5 years from their release date, although most melt over the first year. During their lifetime most, but not all bergs, overturn several times. Our model shows good agreement with the limited observational data. We therefore suggest that icebergs, both modelled and observed, may be exploited as previously little-used geophysical tracers.