US President Donald Trump and Russian President Vladimir Putin have been circling one another, intrigued yet at a distance, ever since the former real estate tycoon launched his convention-busting White House bid.

This week they will come face-to-face in one of the most keenly awaited meetings between two heads of state in years, one that is rich with political, geostrategic and personal storylines.

At the G20 summit in Germany, Trump will greet the man believed by US intelligence agencies to have conceived an intelligence plot to disrupt last year's election and to help him take power.

Over the last four years, Trump has lavishly praised Putin, reviled by most of Washington as a US enemy; noted that the Russian leader has been "very nice" to him and denied his own previous claims that they have met before.

Putin, a former KGB officer who has put a bid to reassert Russian influence at the West's expense at the center of his foreign policy, has described Trump as "bright and talented" but warned that America is in the grip of political "schizophrenia" over allegations that Trump had shared top secret information with visiting Russian officials.

The extraordinary circumstances and political implications of their talks in Hamburg will ensure that their meeting later this week, and any encounter before the cameras in less-formal moments of the G20, is highly scrutinized.

But there's an added dimension to the encounter simply because it involves Putin and Trump.

Both men are well-known for using swaggering machismo at public appearances to intimidate opponents and project an image of strength, aware of the key role of body language in creating a political narrative.

"(I expect) an Olympian level of macho posturing between these two leaders, who both understand the importance of symbolism and the perception of being tough," said Derek Chollet, a former senior national security official in the Obama administration now with the German Marshall Fund.

Trump is under extreme political pressure to raise the issue of alleged Russian interference in the 2016 election.

He must also avoid any impromptu interaction with Putin that would play into his opponents' claims that he is somehow under the Russian leader's influence at a time when a special counsel is investigating whether there was any collusion between his aides and Russian officials before the election.

Putin has used optics before to express his displeasure with US presidents. In 2013, for example, tensions between him and then-President Obama were obvious as both sat stone-faced before the press at a photo op during a meeting in Northern Ireland. Obama later commented that Putin sometimes slouched "like the bored kid in the back of the classroom."

Even without the election question, the meeting between Trump and Putin is key for the future of Europe and the Middle East. The question of US sanctions against Russia for its incursion into Crimea, the future of Syria after the impending fall of ISIS and how to prevent American and Russian forces active in the country from clashing, and willingness of the US to stand by NATO allies are all in the balance.

Who has the upper hand?

In some ways, Trump comes into the meeting at a disadvantage. He is weakened at home, barreling from one self-inflicted political firestorm to another, leaving limited room for maneuver on foreign policy.

Putin, who doesn't have to worry about the checks and balances on power constraining Trump, has established himself as a major world force, expertly playing a weak hand to reassert Russia's influence in Europe and the Middle East, while he exploits fissures in the transatlantic relationship.

Any public grandstanding between the two leaders will grab the headlines.

But the talks have a crucial strategic purpose, since they take place with relations between Russia and the United States in their most dangerous state since the Cold War.

Both men have an obligation to try to halt an alarming trajectory that has their nations brushing up against each other on opposite sides of Syria's civil war, at odds over NATO expansion, and maneuvering troops, ships and planes in dangerous proximity in Europe and the Baltic, with the potential for miscalculation and escalation a daily threat.

"The momentum in relations between the world's two big nuclear powers is now so negative, that it really is time to call a halt to anything that looks like further escalation or deterioration," said Matthew Rojansky, director of the Kennan Institute at the Woodrow Wilson Center.

"That's really only possible at the presidential level," he added.

Better relations with Russia -- is it possible?

The political hoopla surrounding the meeting means that significant progress is unlikely — even if the White House is trying to play down the spectacle.

"It won't be different from our discussions with any other country, really," said National Security Adviser H.R. McMaster at a briefing for reporters last week.

That deadpan statement is inconsistent with the most intriguing aspect of the encounter — it remains unclear whether Trump shares the consensus within his own national security team and in Washington that Russia is an adversary.

Although he said in January that "I think it was Russia" in reference to election meddling, Trump has more frequently dismissed the idea his aides colluded with Russia as a "hoax" perpetrated by Democrats and the "fake news" media dismayed at Hillary Clinton's defeat last November.

Trump has also repeatedly called for improved ties with Russia. He is not the first President to do so: George W. Bush and Barack Obama came into office hoping to do the same, but found that competing national interests squelched their hopes of forging personal connections with their Russian counterparts.

Trump also lavished personal praise on Putin, several times arguing he was a better leader than Obama.

"I would love to be able to get along with Russia," Trump said during a news conference in February.

Election meddling?

For US observers, the big question is whether Trump will use the meeting to complain about election interference.

A failure to do so would be a political loser at home since critics will charge him with abdicating his responsibility to preserve the integrity of American democracy.

But both McMaster and Trump's top economic adviser, Gary Cohn, punted last week.

"There's no specific agenda. It's really going to be whatever the President wants to talk about," said McMaster.

The White House's refusal to offer details of the format of the meeting reflects its political sensitivity.

"We don't know if it will be a long bilateral meeting, or a shorter pull aside at this stage. Those details haven't been set so in part that format of that meeting will dictate what they discuss and how they discuss it," said Thomas Bossert, a White House homeland security adviser on ABC's "This Week" Sunday.

It is not even clear yet whether Trump and Putin will appear together before the cameras. The White House may want to avoid the kind of bad optics seen when the President was shown grinning with Russian Foreign Minister Sergey Lavrov and Ambassador Sergey Kislyak at an Oval Office meeting in May.

US commitment to NATO

But there's more than Trump's political hide at stake.

US allies also have a big stake in the talks and Trump could chose to appease them in a way that could also help his own political plight before he meets Putin by making a strong statement of support for the Western alliance while he is in Poland before the G20.

Trump dismayed European leaders by failing to reaffirm Article 5, NATO's mutual self-defense principle, while in Europe in May. Although he did so in a later White House press conference, suspicion about his motives is still rife.

But a strong pro-NATO statement could make it clear to Putin that Trump's America can't be pushed around after the election interference episode.

"The President has the wherewithal and the willingness to deter President Putin from any more of this behavior," said former US Assistant Secretary of State Jamie Rubin.

"That is why all this talk about NATO is so important. If President Putin doesn't believe that Donald Trump and his NATO allies are in sync and agree and will fight together for their joint purposes ... he won't be deterred," Rubin told CNN's Brooke Baldwin Friday.

But with both sides locked in escalating military tensions in Europe and at odds over Ukraine, it is crucial that they stop tensions from getting worse.

"It's vital," Rojansky said, "they preserve the ability to meet at their level in the future in order to transcend the political and technical hurdles the two governments will inevitably encounter at working levels."