When will the polar ice caps melt and what will happen when they do?

I have good news and bad news.

The good news is that the Antarctic ice caps aren't going to melt away completely any time soon. They're simply far too thick; they go down for kilometers.

The bad news is that the Arctic ice cap is going to melt away quite soon---at current rates of global warming, most scientists believe it will be effectively gone in about 30 years. The other bad news is that the Antarctic ice caps are in fact melting, and they will soon start contributing huge amounts of water to the oceans.

As the ice caps melt, the sea level will rise. If all the ice in Antarctica melted (which, let me repeat, will take a very long time), global sea levels would rise some 70 meters---that's almost as tall as the Capitol Building. This wouldn't completely flood the world---most of the land will still be here---but it would flood almost every coastal city in the world, which turns out to be an awful lot of cities. New York, Boston, Los Angeles, San Francisco, London, Amsterdam... they'll all be underwater unless global warming is stopped or huge dikes are built around them (actually Amsterdam already has dikes---but they'll need much bigger ones). Fortunately we have a fair amount of time to adapt; sea levels currently only rise about 3 millimeters per year, so it'll take about a century for them to rise one foot.