Former Vice President Kamala Harris’s account of tension with former President Joseph R. Biden Jr. in her new book about last year’s campaign to be published Tuesday is revealing, intriguing and even sensational. But it is not uncommon.

American history is replete with partnerships between presidents and vice presidents that broke down in mutual acrimony. In modern times, in fact, the relationships between the past five presidents and their vice presidents all turned notably sour by the end in ways that had lasting consequences.

It probably should come as no surprise that presidents and vice presidents are at times frenemies. They are often party rivals who team up out of political expediency to win an election, much as Mr. Biden and Ms. Harris ran against each other for the Democratic nomination in 2020 before he tapped her as his running mate. Inevitably, both want the same job, but only one can have it at a time.

In her book, “107 Days,” Ms. Harris touches on the strain with the president during their four years together — and its revelations may exacerbate them. Ms. Harris spoke with Mr. Biden recently, according to a person familiar with the conversation, to give him a heads-up before an excerpt from the book ran in The Atlantic in which she wrote that it was “recklessness” for Democrats to let Mr. Biden decide to run for a second term without weighing in. But the excerpt generated angry blowback from Mr. Biden’s loyalists and it was not clear if the two have spoken since.

Here is a short history of the fraught relationships between presidents and vice presidents.

The Early Years

Under the original Constitution, the vice president was not the running mate of the president but the second-place finisher in the Electoral College, making competition inevitable. In 1796, Vice President John Adams was elected the nation’s second president by beating Thomas Jefferson, who then became his vice president.

For four years, the theoretical partners in governing represented the two competing factions of the age, taking opposing positions on domestic and foreign policy. Jefferson even secretly wrote the Kentucky Resolution protesting the Alien and Sedition Acts, which were signed by Adams. The two then ran against each other again in 1800, and this time Jefferson won.

Except it wasn’t quite that simple either. Jefferson’s putative running mate that year, Aaron Burr, also outpaced Adams and ended up with the same number of Electoral College votes as Jefferson. When the tie result went to the House to be resolved, Burr schemed behind the scenes to take the presidency away from Jefferson but came up short.

That left Burr as vice president for the man he had betrayed. Not surprisingly, Jefferson ignored him for four years and then dumped him for his second term in 1804. Later he even put Burr on trial for treason for trying to carve off western territories as a new breakaway nation, although Burr was acquitted. The 12th Amendment, ratified in 1804, changed the way vice presidents were picked so they would always be part of the same ticket as presidents.

Even so, President Andrew Jackson and his vice president, John C. Calhoun, clashed too, particularly over a hotly disputed tariff. Calhoun argued that states like his home of South Carolina had the right to nullify federal laws like the tariff, while Jackson threatened to use force to ensure compliance, bringing the country close to civil war decades before the eventual secession crisis.

Calhoun grew so openly rebellious against Jackson that he even cast the tiebreaking vote in the Senate killing his own president’s nomination of Martin Van Buren as ambassador to Britain. Jackson later replaced Calhoun on the ticket for a second term in 1832 with Van Buren.

20th Century Rifts

Franklin D. Roosevelt overcame John Nance Garner for the Democratic nomination in 1932 and then made him his running mate to bring the party together. But the new conservative vice president from Texas criticized parts of the liberal New Deal and later opposed the president’s plan to pack the Supreme Court.

Garner bristled at the idea that Roosevelt would run for an unprecedented third term in 1940 and sought the Democratic nomination himself. After Roosevelt pushed Garner aside to secure renomination, he replaced him on the ticket with Henry Wallace — and then dumped Wallace four years later for Harry S. Truman.

Likewise, John F. Kennedy offered the vice presidency to Lyndon B. Johnson after surpassing him for the Democratic nomination in 1960. But Johnson was never in the inner circle in the Kennedy White House and resented it deeply. After Kennedy was assassinated and Johnson became president, his acrimonious relationship with Robert F. Kennedy tore Democrats apart in the 1960s.

While bitter about his treatment as vice president, Johnson was not much better to his own partner, Hubert Humphrey. After Johnson dropped out of the race for re-election in 1968, Humphrey stepped up but felt constrained from distancing himself from the unpopular president over the war in Vietnam until late in the campaign and lost narrowly on Election Day.

Gerald R. Ford, who also served as vice president and considered it the most miserable period of his life, appointed Nelson Rockefeller to replace him after becoming president following the resignation of Richard M. Nixon. But Rockefeller was too liberal for many Republicans, and Ford took him off the ticket in 1976 to win conservative support to secure the party nomination, only to lose in the general election.

Clinton-Gore

Bill Clinton and Al Gore were initially seen as a politically ideal pair: both bright, young Ivy League-educated Southern Democrats representing a new generation. But by the end, they had a falling-out over the sex scandal that led to Mr. Clinton’s impeachment. As he ran to succeed Mr. Clinton in 2000, Mr. Gore picked a critic of the president as his running mate and declined to dispatch Mr. Clinton to campaign in key states where he might have made a difference.

After the Supreme Court ended a recount in Florida, finalizing Mr. Gore’s defeat, the vice president confronted the president in the Oval Office in a heated argument marked by mutual recriminations. Mr. Gore blamed his loss on Mr. Clinton’s scandal, while the president pushed back and faulted his vice president for not running on the administration’s record of successes.

Bush-Cheney

George W. Bush relied heavily at first on his seasoned vice president, Dick Cheney, who was seen as perhaps the most powerful person ever to hold that office. But despite the common impression, Mr. Bush increasingly disregarded Mr. Cheney’s advice by his second term, with the two disagreeing on issues like Iran, North Korea, climate change and same-sex marriage.

Mr. Cheney did not run to succeed Mr. Bush but, like Mr. Clinton and Mr. Gore, he clashed with the president in the Oval Office in their final days in the White House. Mr. Cheney pressured Mr. Bush for a pardon for the vice president’s former chief of staff, I. Lewis Libby Jr., who had been convicted of perjury in a case about the public disclosure of a C.I.A. officer’s identity. When Mr. Bush refused, Mr. Cheney lashed out, saying it was dishonorable to “leave a soldier on the battlefield.”

Obama-Biden

Few presidents and vice presidents were as different temperamentally, politically and generationally as Barack Obama and Mr. Biden, but the two forged an unlikely friendship while in office. Mr. Obama even offered his own money to Mr. Biden when the vice president was financially stressed over medical bills for his dying son.

But the two split over Mr. Obama’s decision to support Hillary Clinton, not Mr. Biden, as his successor in 2016. Over lunch, Mr. Obama tried to gently persuade Mr. Biden not to run, alienating the vice president and marring their relationship for years. Mr. Biden went on to run and win in 2020, but after his disastrous debate performance in 2024, he believed Mr. Obama was working behind the scenes to push him out of the race.

Trump-Pence

No partnership between a president and vice president has blown up quite as explosively as that between Donald J. Trump and Mike Pence. While the stoic Mr. Pence was relentlessly deferential to the bombastic Mr. Trump for nearly four years, the vice president finally broke with the president over his efforts to reverse the results of the 2020 election.

Mr. Trump pressured Mr. Pence while the vice president was presiding over the congressional counting of Electoral College votes to disallow slates from swing states that went for Mr. Biden. Mr. Pence refused to go along, deeming it unconstitutional. When a mob of Trump supporters stormed the Capitol on Jan. 6, 2021, to try to stop the count, they chanted, “Hang Mike Pence,” and the vice president had to be evacuated for his safety. Aides said that Mr. Trump told them at the White House that maybe the mob had it right.

With the approach of the 2024 campaign, Mr. Pence became the only vice president other than Mr. Garner to run against the president who selected him, but he gained no traction in the Republican nomination contest. After dropping out, Mr. Pence refused to endorse Mr. Trump in the general election that fall against Ms. Harris.