(CNN) Fidel Castro visited the United States only a handful of times. But the late Cuban dictator for decades had an outsized effect on the presidential politics of his northern neighbor.

Castro, who died late Friday, long befuddled American administrations, Republican and Democratic. Commanders in chief found they had limited options against the bearded leader of an island nation just 90 miles off America's southern shores.

His country in 1962 famously became the nexus of a near-nuclear Armageddon during the Cuban missile crisis. The 13-day Cold War-era standoff calmed only when Soviet Premier Nikita Khrushchev backed down against President John F. Kennedy's administration, removing nuclear warheads from Cuba.

More recently President Barack Obama sought to thaw years of hostility between the US and Cuba. On December 17, 2014, Obama and Cuban President Raúl Castro (Fidel's younger brother and appointed successor) began the process of normalizing relations for the first time since they were severed in 1961.

Here are five ways Fidel Castro influenced American presidential politics and government, overtly and indirectly.

Bad first impressions

Castro wasn't immediately labeled an enemy after his leftist forces overthrew the Cuban leader Fulgencio Batista on January 1, 1959. Castro visited the US in mid-April to address the American Society of Newspaper Editors and the Council on Foreign Affairs.

The GOP administration of President Dwight Eisenhower also wanted to size up Castro. While Eisenhower wouldn't meet the insurgent Cuban leader, Vice President Richard Nixon was dispatched for the task.

It didn't go well.

In the Washington meeting, Nixon hoped to push Castro "in the right direction," he said at the time , away from radical policies. But Castro acted confrontational and standoff-ish, according to American officials, who were used to open access to casinos and sugar cane during Batista's long reign.

The CIA soon began developing plans to arm and train a group of Cuban exiles. This would play out, in failure, amid the April 1961 Bay of Pigs fiasco ordered up by Eisenhower's Democratic successor, Kennedy.

Intelligence ops

Those anti-Castro plans had actually played a role in the hard-fought presidential race between Nixon and Kennedy -- and for decades have influenced the debate about just how much information to give out to presidential candidates on intelligence and national security.

Eight years earlier, during the early Cold War years, presidential candidates for the first time were provided intelligence briefings. The thinking was that the winner shouldn't be caught cold about thorny world problems -- and clandestine operations -- upon assuming power.

In the closing weeks of the 1960 presidential race, the Kennedy campaign released a statement calling for a group of exiled Cubans to retake their country. The nominee was asleep when the statement went out and never saw it, USA Today reported this August

But Nixon, who was running against Kennedy, knew his Democratic opponent had been briefed about Cuba and figured he was aware of their plans for the exiles to attack.

Nixon seethed over the matter. But having been privy to classified information spelling out the Cuban exile plan, he took the opposite view publicly during the campaign in order not to accidentally divulge it.

He did try to get at the issue through a side door, however, in one of four televised debates against Kennedy, then representing Massachusetts in the Senate.

"I think that Sen. Kennedy's policies and recommendations for the handling of the Castro regime are probably the most dangerously irresponsible recommendations that he has made during the course of the campaign," Nixon said during their final face-off.

Nixon narrowly lost the presidency to Kennedy, and for years he nursed a grudge against the intelligence community, suggesting it had aided his rival.

While the precise nature of intelligence on Cuba provided to JFK during the campaign remains murky, it's fair to say the episode played into Nixon's long-standing resentments against the Kennedy family and intelligence officials, which would return to haunt him during his own presidency, from 1969-1974.

Intelligence briefings for presidential candidates remain a sensitive issue. During the 2016 campaign, critics of Republican nominee Donald Trump warned that he might share secret information, on Twitter or elsewhere. And Hillary Clinton's use of a private email server as secretary of state, which the FBI called reckless in its implications for classified information, led for GOP calls that she not receive the briefings.

Exploding cigars?

A decade-and-a-half and three presidencies after Kennedy, Castro's regime still vexed American lawmakers.

In 1975, amid widespread distrust of government after Vietnam and Watergate, the Senate's Church committee probed the CIA and other governmental operations. The panel found that CIA employees had at times run what seemed like a rogue agency, including a batch of assassination attempts against Castro formulated by subordinate employees without their superiors' permission.

Some were borderline comical and ham-handed. Assassination plots reportedly included exploding cigars -- a product favored by the Cuban strongman -- and even a poisoned ballpoint pen.

Critics of the Church committee raged that precious intelligence secrets were being aired publicly, which threatened national security. That approach remained a matter of fierce debate in the post-9/11 era. Defenders of President George W. Bush pushed back against efforts to reveal interrogation methods of terror suspects.

Boatlift politics

Castro, if indirectly, nearly prevented the Bill Clinton presidency from ever happening. In 1980, the Cuban dictator startled American officials by allowing a mass emigration from the island, which became known as the Mariel boatlift.

The exodus included not just political exiles but a bunch of refugees that had been released from Cuban jails and mental health facilities. President Jimmy Carter's administration housed some of these people in Arkansas, just as Clinton, the nation's youngest governor, was running for re-election.

On June 1, 1980, a riot broke at Fort Chaffee, a military installation in Arkansas where the Cubans were being housed. And locals weren't happy about it, noted The Washington Post 35 years later , in the midst of Hillary Clinton's presidential campaign.

"The White House message seemed to be: 'Don't complain, just handle the mess we gave you,'" Clinton, first lady of Arkansas in 1980, later wrote in her memoir "Living History."

"Bill had done just that, but there was a big political price to pay for supporting his President," she said of her husband's acquiescence to the plan by a fellow Democrat in the White House.

Bill Clinton lost his re-election bid, making him the youngest ex-governor in the country. He then won back the office two years later, setting up his successful White House run a decade down the line. But Clinton long nursed a grudge against Carter, who lost the White House to Ronald Reagan in 1980.

Cuban boy hurts Al Gore's hopes

Castro's death Friday came 17 years to the day after the rescue of a five-year-old Cuban boy, Elián Gonzalez. Fisherman found the child clinging to an inner tube three miles off the coast of Ft. Lauderdale, Florida, after his mother and 11 others perished in their attempt to flee Cuba for the US.

A protracted seven-month standoff between American and Cuban authorities followed -- in the shadow of a tight presidential race.

In an April 2000 pre-dawn raid, armed US federal agents seized Gonzalez from the home of his Miami relatives, who wanted him to stay in the US even as the government said he needed to return to Cuba.

Within a few hours, the boy was reunited with his father, who had come to the US to plead for his return. Two months later, after a swath of court procedures and anti-Castro demonstrations, they returned to Cuba.

Many in the Cuban-American community blamed the Clinton administration for turning the child over to the communist nation. After all, Attorney General Janet Reno had put in place the legal mechanisms for doing so -- which she defended as a family reunification measure prescribed by law.

Vice President Al Gore, the Democratic nominee that year, came in for harsh criticism. He ended up losing Florida -- and the presidency -- to Bush, then governor of Texas, by an official count of 537 votes out of more than 6 million cast.

While it's impossible to ascribe one factor to Gore's razor-thin defeat, the Elián Gonzalez effort likely ginned up voting among South Florida's stridently anti-Castro Cuban-American population. That's the working theory, at least, of author Jeff Greenfield, in his counter-factual historical eBook novel "43: When Gore Beat Bush."

Greenfield, a five-time Emmy-winning network television analyst, posits that had Elian Gonzalez's mother not died in the journey from Cuba, that matter never would have become such a public spectacle -- and that many voters in the Cuban-American community would not have been enraged at the Clinton administration.

Greenfield noted that Gore received only about 20% of Cuban-American votes in 2000, according to exit polls, while Clinton won about 35% in his 1996 re-election bid.

Sixteen years later, in the waning days of Castro's life, he continued to feature in American presidential politics.

Trump, on his way to an upset victory over Hillary Clinton, pledged on the campaign trail to unravel the Obama administration's détente with Cuba.