The 25th Amendment, ratified in 1967, solved the problem of how to replace a vice president. If Cheney resigned, President Bush would select a nominee for the vice presidency. Then the nominee would have to be approved by majority votes in both the House and the Senate.
Before the 25th Amendment, a vacancy in the office was simply left unfilled. The impetus for the 25th was the assassination of John F. Kennedy–with Lyndon Johnson’s ascension to the presidency, there was no vice president in place in case something befell Johnson. Then-Rep. Gerald Ford was appointed under the 25th following the resignation of Vice President Spiro Agnew in 1973. In 1974, after Richard Nixon resigned, Ford became president and selected Nelson Rockefeller as vice president. After a long congressional inquiry, Rockefeller was approved, making them the country’s first nonelected president and vice president.