At present the biggest uncertainty in future sea level rise lies in the unknown contributions from melting land ice. Recent measurements by the GRACE satellite gravity mission suggest an accelerated melting of the Greenland ice sheet, ice mass loss in West Antarctica and significant contributions from glaciers in Alaska, Patagonia and in the Canadian Arctic Archipelago. We model the response of the global and regional sea level to the anomalous input of melt-water on the background of ongoing thermal expansion induced by global warming. Local density decrease leads to regional and global changes of the ocean circulation and oceanic transports of heat. This in turn will induce atmospheric feedback. Relative sea level change such as measured by coastal tide gauges is influenced additionally by the elastic movement of the solid Earth and geoid change in response to present day variations in the mass distribution on the background of the viscoelastic response of the earth's crust due to past deglaciation. Typical patterns of sea level change due to different sources of melt-water input are identified. Local deviations from the global mean are located predominantly close to the source regions of ice melt. An attempt to determine melting rates from satellite altimetry and - gravimetry is presented.