But things are different this year.
Establishment Republicans are quite open about the fact that they want a contested convention; they simply can't stomach Donald Trump.
And on the Democratic side, Bernie Sanders's staff acknowledged this week that the senator from Vermont hopes he can win the nomination at a contested convention.
It's impossible to say whether either party will actually get to that point in 2016. Trump could wrap up the GOP nomination by winning about 63 percent of the remaining pledged delegates. Sanders faces an uphill battle to stop Hillary Clinton from winning the nomination with pledged delegates alone; her overwhelming support from superdelegates is likely to put her over the top on the first ballot either way.
But the possibility that at least one party goes to a contested convention is real. So what might that look like? Historically, contested conventions have gone a lot of different ways. Here are just a few of the most fiery conventions in U.S. history.
Democratic National Convention, 1860
The 1860 Democratic convention, just before the Civil War, was divided over slavery. Sen. Stephen A. Douglas, considered a moderate on the slavery issue because he preferred to let individual states choose whether to outlaw or allow the practice, was the front-runner. But delegates from seven southern states organized an effort against him, and he couldn't get the requisite number of votes.
After holding a convention in Charleston, S.C., where delegates were unable to come to any kind of consensus after 57 ballots, Democrats took six weeks off before trying again in Baltimore, where Douglas was nominated. But the splinter group of southern Democrats didn't attend; they held their own convention, and nominated Vice President John C. Breckenridge. Thus, two Democrats were nominated, and Republican Abraham Lincoln beat them handily that November.
It seems pretty unlikely that a group of state delegations would break off from their national party apparatus to hold their own convention in 2016, but seeing two of the current GOP candidates on November's ballots isn't completely out of the question if one of them decides to run as an independent.
Democratic National Convention, 1924
The 1924 Democratic National Convention, held in New York, was the longest-running political convention in U.S. history. The party was divided, again largely on geographic lines, at a time when the Ku Klux Klan was rapidly gaining political power.
Pro-Klan delegates from the South and other areas couldn't see nominating New York Gov. Al Smith, a Catholic. But anti-Klan delegates were against nominating William Gibbs McAdoo, who had Klan support despite not being a member. There weren't enough delegates in either faction to nominate a candidate, so the voting went on and on.
Eventually, after 102 ballots, McAdoo and Smith both withdrew from consideration, knowing they'd never get the requisite votes. A compromise candidate, John W. Davis, got the nomination, but lost in the general election by almost 250 electoral votes.
Some Republicans hope they can find a compromise candidate this summer – the name Paul Ryan keeps coming up, despite him saying he doesn't want to run – but as the 1924 convention shows, a compromise candidate isn't guaranteed the enthusiastic support of the entire party. In fact, it's possible that few voters would be excited about a compromise candidate.
Republican National Convention, 1964
Like in the Democratic convention of 1924, Republicans were split among geographic and ideological lines at their 1964 convention. The moderate wing of the GOP was in favor of Nelson Rockefeller, the Republican governor of New York, who would later go on to serve as vice president under Gerald R. Ford. Conservative Republicans, on the other hand, preferred Barry Goldwater, a hawk from Arizona who wanted to undo everything he could about Franklin D. Roosevelt's New Deal programs.
Conservative Republicans openly booed Rockefeller at the convention because they thought he was part of the northeastern political elite – the GOP establishment. Sound familiar?
Goldwater, on the other hand, took hard-line positions on limited government and opposing the relatively new communist government in Vietnam. Moderate Republicans openly disliked him, and some viewed him as such an extremist that his hard-line stances were thought to damage his chances in the general election. Goldwater lost to Lyndon B. Johnson.
Democratic National Convention, 1968
Perhaps the most violent, vitriolic and widely-known turbulent convention in American history was the 1968 Democratic National Convention in Chicago. This time, it wasn't about an electorate divided between two candidates — it was about tension that had been building for months exploding into violent riots.
The Rev. Martin Luther King Jr. was assassinated that spring. Robert F. Kennedy, one of the leading candidates, was killed even closer to the convention, on June 5. And the Vietnam war was at its peak.
So when an estimated 10,000 antiwar demonstrators descended on the city, Chicago Mayor Richard J. Daley simply decided not to issue permits. He thought, naively, that without a place to gather, the protests would remain small. But still, he was able to deploy about 23,000 police and National Guard members, and he wasn't afraid to use them.
Things went fairly smoothly in the convention hall, and Hubert H. Humphrey won the nomination handily. But outside the hall, Daley's aggressive response to the protesters turned an already volatile situation into a violent one. On Aug. 28, 1968, the day of the so-called "police riots," officers moved into the throng of protesters to arrest a man seen lowering an American flag. The officers beat the protester, while other protesters started throwing rocks and chunks of concrete at the police.
The protest quickly turned into a riot and spread throughout the city. One particularly tense exchange took place outside a Hilton hotel, where network television cameras broadcast 17 minutes of the riots live, as protesters chanted, "The whole world is watching!" Television coverage alternated between the relatively straightforward convention and the chaos in the streets, making it appear as though the Democratic Party was anything but unified and connected with its constituents. Humphrey would go on to lose to Richard M. Nixon in the general election.