Twenty-second Amendment to the United States Constitution
Some argue that the 22nd Amendment and 12th Amendment bar any two-term president from later serving as vice president as well as from succeeding to the presidency from any point in the presidential line of succession. Others contend that the original intent of the 12th Amendment concerns qualification for "service" (age, residence, and citizenship), while the 22nd Amendment, concerns qualifications for "election", and thus (strictly applying the text) a former two-term president is still eligible to "serve" as vice president (neither amendment restricts the number of times an individual can be elected to the vice presidency), and then succeed to the presidency to serve out the balance of the term (though prohibited from running for election to an additional term).
President of the United States
Some presidents have had significant careers after leaving office. Prominent examples include William Howard Taft's tenure as Chief Justice of the United States and Herbert Hoover's work on government reorganization after World War II. Grover Cleveland, whose bid for reelection failed in 1888, was elected president again four years later in 1892. Two former presidents served in Congress after leaving the White House: John Quincy Adams was elected to the House of Representatives, serving there for seventeen years, and Andrew Johnson returned to the Senate in 1875. John Tyler served in the provisional Congress of the Confederate States during the Civil War and was elected to the Confederate House of Representatives, but died before that body first met.