Thermal expansion is producing about half of the current 3mm/year increase in global sea level. This contribution has increased from around 0.5 mm/year over the second half of the 20th century to around 1.6 mm/year over the last 12-14 years. This contribution is expected to continue at least at this level over the next century or more due to greenhouse-gas-induced warming of the atmosphere and ocean.
Due to the very patchy and sparse (especially as we go back in time) body of ocean temperature data that is available to estimate longer-term contributions, the contribution over most of the 20th century is hard to estimate reliably.
A major contribution to recent sea level rise is from the melting of glaciers, and contributions from the Greenland (both surface melting and iceberg calving and the Antarctic ice sheet (iceberg calving only). This is believed to produce about one third or more of the current 3mm/year annual increase in global sea level. The contribution from the ice sheets is poorly understood at the moment and is an active area of research. The melting of the Greenland ice sheet alone could increase global mean sea level by around 7 metres. This would probably take around 1,000 years, but it is believed that ice melt from Greenland could still contribute significantly to sea level rise over the next 50-100 years.