Section 1. No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once. But this article shall not apply to any person holding the office of President when this article was proposed by the Congress, and shall not prevent any person who may be holding the office of President, or acting as President, during the term within which this article becomes operative from holding the office of President or acting as President during the remainder of such term.
Section 2. This article shall be inoperative unless it shall have been ratified as an amendment to the Constitution by the legislatures of three-fourths of the several States within seven years from the date of its submission to the States by the Congress.
Prior to Franklin D. Roosevelt, only two Presidents attempted to serve for more than two terms, and neither were successful. Ulysses S. Grant sought a third term in 1880 after serving from 1869 to 1877, but he narrowly lost his party's nomination to James Garfield. Theodore Roosevelt succeeded to the presidency upon William McKinley's assassination and was elected in 1904 to a full term himself, serving from 1901 to 1909. He sought to be elected to a third (non-consecutive) term in 1912 first seeking the Republican Party's nomination, and when he was unsuccessful running as a third party candidate, but he lost in the general election to Woodrow Wilson.
In 1940, Franklin D. Roosevelt became the only president to be elected to a third term and in the 1944 election, during World War II, he won a fourth term, but suffered a cerebral hemorrhage and died in office the following year. Thus, Roosevelt was the only President to have served more than two terms.
There have been attempts to repeal the 22nd Amendment including by Rep. Barney Frank, Rep. José Serrano, Rep. Howard Berman, and Sen. Harry Reid, but each resolution died before making it out of its respective committee. Other alterations have been proposed, including replacing the absolute two term limit with a limit of no more than two consecutive terms and giving Congress the power to grant a dispensation to a current or former president by way of a super-majority vote in both houses.
The amendment specifically did not apply to the sitting president Harry S. Truman at the time it was proposed by Congress. Truman, who had served nearly all of FDR's unexpired fourth term and who had been elected to a full term in 1948, began a campaign for another term in 1952, but quit after a poor showing in the New Hampshire primary.
The only individuals who have been prohibited from continuing to seek the presidency under the amendment are Dwight D. Eisenhower, Richard Nixon, Ronald Reagan, Bill Clinton, and George W. Bush, who were all elected to the presidency twice. Former presidents Jimmy Carter and George H. W. Bush, both defeated after only one term (in 1980 and 1992 respectively), are eligible to seek the office again. It's unlikely that in this era of divided and polarized politics, the 22nd Amendment will ever be repealed in our lifetimes.