Who becomes president if both the president and vice president are unable to serve?

The remaining Survivor becomes President or remains President.

If both the president and vice-president die at the same time, the Speaker of the House becomes the President.

When Bush was president, the left liked to joke about "President Pelosi"--supposedly what would happen if both Bush and Cheney were impeached. That wouldn't have happened because in two scenariOS:

One: Bush is impeached and removed. Cheney is elevated. His first act: appoint a vice president. When Cheney is then removed, his new VP becomes president.

Two: Cheney is impeached and removed. Bush appoints a new VP, who becomes president upon Bush's removal.

In either case we're looking at President Grover Norquist, not President Nancy Pelosi.