The last two American presidents tried mightily to improve relations with Russia. President George W. Bush famously said he had "looked into the soul" of Russia's leader Vladimir Putin during a 2001 summit. By the end of his term, Putin had invaded Georgia.

In 2009, President Obama promised a "reset" that dissolved after the 2011 Russian elections and the country's 2014 annexation of Crimea and occupation of eastern Ukraine.

Now comes president-elect Donald Trump, who has been the most pro-Russia presidential candidate in decades. During his campaign, he refused to meet with Ukraine's president, called for U.S.-Russia cooperation in Syria and brushed off U.S. intelligence officials who said that Russia hacked e-mails from the Clinton campaign and the Democratic National Committee.

On Thursday, the Washington Post reported that Kremlin officials maintained contact with Trump team members during the presidential campaign, including meetings with Russian embassy officials in Washington.

A Trump spokeswoman denied the campaign had contacts with Russian officials.

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In his message to the president-elect, Putin on Wednesday said "Russia is ready and wants to restore full-scale relations with the U.S. We understand it will be a difficult path, but we are ready to play our part."

What could go wrong if Trump and Putin stoke a geopolitical bromance?

For one, it probably will fizzle quickly, according to Christopher Chivvis, a former Pentagon analyst under the Obama administration and now senior political scientist at the Rand Corporation.

"If (Trump) does attempt to improve the air, to do a deal with Russia or strengthen the relationship, he will be the third president in a row to try that," Chivvis said. "And he will be the third to fail."

Chivvis said there are actually very few areas of common interest between the two countries. Aiding Russia in Syria means backing a tyrant that has gassed and bombed his own people, among other things, and led to a huge flood of Syrian refugees that has enveloped Europe.

If Trump decides supporting Ukraine against Russian aggression isn't worth it, that could send a ripple across the region, Chivvis said.

"Countries elsewhere in the region would begin to doubt the extent to which the United States is committed to their security," he said.

Putin may also be trying to buddy up to Trump in order to lift economic sanctions, which President Obama and European leaders imposed after the Ukraine invasion. While the United States doesn't have a lot of direct trade with Russia, countries like France do and have been pushing to get them eased.

"If the belief is that the United States is not behind the sanctions, even before Trump takes office, we could see those sanctions getting very shaky by the end of the year," Chivvis said.

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But perhaps a bigger concern for Americans is whether Trump's election and his dismissal of concerns about Russian hacking during the campaign would give the green light to Russian-sponsored hackers to cause more trouble here at home.

"What they'll learn from this is, 'We did it, we got away with it, we got the outcome we wanted,'" James Lewis, a cybersecurity-focused fellow with the Center for Strategic and International Studies, told Wired. "This will only increase their desire to intervene," he said.

Despite fears, there was no reports of Russia-based hacking during Election Day itself. And one Russia expert says that the earlier leaks of e-mails designed to embarrass Clinton campaign officials may have been done as a form of competition by lower-level cyber-agents at various Russian intelligence agencies.

"It was not Putin sitting in the Kremlin saying, 'Let's try to compromise Clinton's emails and give them to Trump,'" said Alexander Baunov, associate fellow at the Carnegie Endowment for Peace's Moscow Center and a former Russian journalist. "Some hackers gave material to their supervisors, and the supervisors gave the material to those above them and said, "What if you published some and see the reaction?'"

Baunov says the leak was a mistake, because it could have backfired had Clinton been elected.

As it stands, there's still a lot of bad feelings between the two countries, which won't be easily dismissed by a few pro-Putin comments by Trump.

"The history of relations between United States and Putin's Russia is already very toxic," Baunov said. "From Putin's perspective, it was he who tried to make better relations to the West and was rejected again and again. Many Russians feel the same."

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