If ever there was a roller-coaster of a relationship it was the one the United States had with Libyan leader Muammar Gaddafi, which went from bombing to befriending to supporting bombing again.
But after decades of bloodshed and turmoil, the U.S. reaction to Gaddafi's death during a battle for his hometown of Sirte could be summed up in one word: relief.
"I think it's about time," Republican presidential candidate Mitt Romney told reporters in Sioux City, Iowa. Gaddafi was "a terrible tyrant that killed his own people and murdered Americans and others in the tragedy at Lockerbie. The world is a better place with Gaddafi gone."
If Gaddafi had survived the war with the Libyan opposition forces who are now internationally recognized as the new government, it could have started yet another downward cycle with the United States.
"Gaddafi was a major threat to the United States up until a few years ago, and if he had survived this regime change, he very well could have continued to be a threat since he would have blamed us for his demise," said Darrell West, director of governance studies at The Brookings Institution.
How three different U.S. presidents handled the mercurial man who seized power in Libya in a 1969 coup illustrates the tempestuous journey of U.S.-Libyan ties.
A generation ago, President Ronald Reagan called Gaddafi the "mad dog of the Middle East," and named Libya a suspect in the deadly 1986 bombing of a West Berlin discotheque frequented by members of the U.S. military.
About a week later, U.S. military jets struck Libya, hitting a Gaddafi compound in Tripoli and reportedly killing his adopted baby daughter. Reagan said: "Today we have done what we had to do; if necessary, we will do it again."
Gaddafi, in short, was a U.S. nemesis long before al Qaeda chief Osama bin Laden or Iraqi dictator Saddam Hussein, whom he joins in death.
U.S. animosity toward Libya intensified further after the 1988 bombing by Libyan agents of a Pan Am airliner over Lockerbie, Scotland, that killed 270 people.
But over a decade later the ice started to thaw under President George W. Bush after Gaddafi promised in 2003 to give up his weapons of mass destruction and completed a compensation settlement for the families of the Lockerbie victims in 2008.
Bush is believed to be the first U.S. president to speak to Gaddafi when he phoned the Libyan leader in November 2008 to express satisfaction about the Lockerbie claims settlement.
Diplomats and businessmen flocked to Libya in greater numbers. Famous U.S. entertainers performed for the Gaddafi clan. Secretary of State Condoleezza Rice met Gaddafi in Tripoli in 2008.
But when the rebellion against Gaddafi's rule began earlier this year, the United States demonstrated how tenuous the relationship had been. It backed the rebels against a fierce onslaught by Gaddafi's forces. President Barack Obama came out and said Gaddafi must go.
On Thursday, in a statement after Gaddafi's death, Obama declared: "You have won your revolution."
Under Obama, the United States played a mostly supporting role in NATO military operations over Libya. As far as is known, Washington had no direct role in his death.
Others nonetheless saw the events as a fulfillment of the long, winding road of U.S. policy on Libya.
"It completes the Reagan legacy, he called him the mad dog of Tripoli and tried to kill him," Lawrence Korb, senior fellow at the Center for American Progress, said. "Yes he was welcomed back into the international community in 2003, but even so I think they had to hold their nose when they did it."
The biggest relief was likely felt by the Lockerbie families. "I hope he's in hell with Hitler," said Kathy Tedeschi, whose husband was killed on Pan Am Flight 103.
Along with antagonism toward Gaddafi, his eccentricities, such as having a tent pitched on property owned by New York real-estate magnate Donald Trump ahead of the U.N. General Assembly, became fodder for American jokes.
"He seemed very strange, but yet the guy maintained his hold on office over a very long period of time, and so he clearly was more wily than people gave him credit for. He survived most other leaders on the world stage," West said.
Gaddafi's death did not provoke the same jubilation in the United States as the killing of bin Laden, when crowds gathered outside the White House chanting "USA, USA."
But it was generally welcomed among the smattering of tourists meandering outside the White House on Thursday.
"It's good news," said Dan DeBoise, 49, a nurse from Spokane, Washington. "The U.S. constantly feels like we need to police the world and the less bad guys out there it's going to be better."