While flights over the North Pole connecting Europe, North America and Asia have become fairly commonplace, up to now, no airline has planned a route that crossed Antarctica. That may be about to change with a planned route from Buenos Aires to Perth, Australia.
Norwegian Air Argentina has applied to Argentina's regulators for permission to fly that route, passing across the center of the 'white continent,' which has almost no infrastructure, and no airport to handle an emergency landing by an airliner. Over the years, the range allows by ETOPS (Extended Twin-Engine Operations) has grown from requiring planes to be within 60 minutes of an airport to 330 minutes, making the route possible.
Norwegian's plan is to use Perth as a connection and fuel stop on the way to Singapore. It will still need permission from Australia and Singapore. But if you're anxious to look out the window and see Antarctica, there's a way: Antarctica Flights runs sightseeing overflights on a 12-hour route from three Australian cities using chartered Qantas 747s, such as the one in picture above.