What Happens If The President And Vice President Both Die?

In the event that both the president and vice president of the United States were to die, the Speaker of the House of Representatives would assume the presidency, followed by (in order):

President pro tempore of the Senate
Secretary of State
Secretary of the Treasury
Secretary of Defense
Attorney General
Secretary of the Interior
Secretary of Agriculture
Secretary of Commerce
Secretary of Labor
Secretary of Health and Human Services
Secretary of Housing and Urban Development
Secretary of Transportation
Secretary of Energy
Secretary of Education
Secretary of Veterans Affairs
Secretary of Homeland Security

as specified by the United States Constitution and the Presidential Succession Act of 1947 (3 U.S.C. § 19) and subsequent amendments to include newly created cabinet officers.

Of course, any person assuming the position of President would have to qualify for the presidency per constitutional specification:

Persons who are not natural-born citizens are constitutionally ineligible to the office of President, as are persons who are not at least thirty-five years old or have not resided in the United States for fourteen years. This is specified in the Presidential Succession Act
(3 U.S.C. § 19(e)).

As well...
To be in the line of succession, an officer must have been appointed and confirmed by the United States Senate, prior to the death, resignation, removal from office, inability, or otherwise failure to qualify of the President pro tempore. Therefore, acting officers who have not been confirmed into the position can

The Speaker of the House who currently is Nancy Pelosi. Isn't that a totally scary thought?

If the Vice President becomes president, he immediately nominates a VP, (who must be confirmed). This new VP would then be president if the new president were incapacitated. If both the president & VP were simultaneously incapacitated, then the speaker of the house would be president.

Below is a link to a government website explaining this in greater detail. I hope this helps!

usinfo.state.gov

Speaker of senate becomes president