The last time that Donald Trump and Vladimir Putin met, four months ago, both the U.S. and Russian presidents reiterated that they were committed to shifting the tone of relations between the two nuclear powers, relations that were already spiraling downward.
The White House and the Kremlin discussed scheduling a second meeting of the two leaders on the sidelines of a November 10-11 Asian-Pacific leaders' summit in Vietnam, but that was ruled out by the White House as Trump arrived in Danang early on November 10.
Still, both the Kremlin and the White House said a less formal encounter was still possible or even likely if Putin and Trump "bump into" each other in Danang or later at another regional conference in the Philippines.
Since their first encounter, relations have deteriorated significantly.
The Trump administration faces a drumbeat of U.S. investigations into alleged Russian meddling in the 2016 election and interactions between Trump campaign staff and Russian officials. A Justice Department probe resulted recently in two criminal indictments and a guilty plea from former Trump advisers.
Congressional pressure has also mounted on Trump to punish Moscow for the suspected election interference, including through sanctions signed into law in August that target Russian military and intelligence services. The Pentagon has also proposed providing lethal aid to Kyiv as it battles Russia-backed separatists that control swaths of Ukrainian territory, a plan that would anger Moscow if it went forward.
For his part, Putin's grip on power at home remains unrivaled. But even with a Russian presidential election four months away and the expectation that he'll win a fourth term in office, the Kremlin might be nervously eyeing the country's continuing economic malaise, rampant corruption, and other issues that could erode Putin's popularity. A former KGB officer whose tenure atop Russian government has spanned four U.S. presidencies, Putin has sought to assert Russian relevance in international affairs from Eastern Europe to Syria and the Korean Peninsula.
"There are things to discuss and we are ready for it," Putin's lead foreign affairs adviser, Yury Ushakov, told reporters in Moscow on November 8 in connection with a possible Putin-Trump face-to-face.
What "things"? Here are a few that could top the agenda of any eventual Trump-Putin meeting:
Trump has made the issue of North Korea's nuclear and missile programs a top priority for his administration. In his diplomatically unorthodox approach, he has exchanged insults and threats with North Korean leader Kim Jong Un.
During the Cold War, Moscow was a stalwart supporter of the North Korean regime, providing subsidies and critical economic support. That assistance dried up with the Soviet collapse, and longstanding personal ties between Russian officials and North Korea's leadership are also said to have withered.
Still, there are those who believe that Russia, which shares a border with North Korea, may be the only country after China that Pyongyang will at least listen to, and Trump is hoping Putin can help bring additional pressure on the North.
In a speech to South Korea's parliament on November 8, Trump signaled that he will press Putin, and China's leadership. He said he wants Moscow and Beijing to fully implement United Nations sanctions, severing trade and technology ties, and downgrading diplomatic relations in order to squeeze Pyongyang.
"You cannot support, you cannot supply, you cannot accept," Trump told South Korean lawmakers.
The fight against international terrorism, and against Islamic State (IS) militants in particular, is an area of potential Russian-U.S. cooperation that Trump has repeatedly heralded. In Syria and Iraq, both U.S. and Russian forces have pounded IS fighters for months now, rolling back their territorial gains, and putting them on the verge of battlefield defeat. But Russian bombardments have also targeted U.S. allies who oppose President Bashar al-Assad's leadership in Damascus.
And competing units on the ground, backed by the two powers and their allies, have operated in close proximity as they consolidate their holdings, and skirmishes have again raised the prospect of an inadvertent clash between U.S. and Russian forces, "de-conflict" efforts notwithstanding.
Moscow and Washington are also on opposite sides of the question of the Syrian government's alleged use of chemical weapons, reported by UN-backed international monitors. The United States and its allies have repeatedly condemned such weapons' use and sought to use the UN Security Council to further pressure Damascus. Moscow, meanwhile, has used its influence to deflect more aggressive UN investigations and condemnation of Syria.
In a statement released on November 9, about a week after international monitors confirmed the use of sarin gas by Syrian forces in an April attack, the White House called Moscow out explicitly in an effort to nudge Russia and other Security Council members to hold Assad's government accountable.
"Those countries that do not support renewal or are attempting to water down the JIM's mandate -- such as Russia -- are protecting the Assad regime and the terrorists who continue to use chemical weapons," Trump's administration said in a reference to the investigation, the so-called UN/Organization for the Prohibition of Chemical Weapons' Joint Investigative Mechanism (JIM). "We urge Russia to change course before the JIM expires, and we believe all responsible nations must vote in favor of extending this critical body."
In Iraq, meanwhile, as Islamic State fighters have been routed, Russia moved quickly to sign major oil deals in the restive Kurdish north, which has historically been closely allied with Washington. Those deals could give Moscow bargaining power at a time when already-tense relations between the Kurds and the central Iraqi government have worsened, and Washington has tried to prevent all-out conflict.
Fighting in Ukraine's east has returned to a slow simmer, with daily exchanges of gunfire but no large-scale fighting. At least 10,000 people have been killed since April 2014, when the conflict erupted between Russia-backed separatists and Ukrainian government troops, and Russia maintains its occupation of the Crimean Peninsula.
To date, the only reasonably successful efforts at a political settlement have been the so-called Minsk agreements, but they have gone largely unfulfilled.
In September, Putin floated the idea of UN peacekeeping forces deploying to eastern Ukraine. But Ukrainian President Petro Poroshenko has insisted that such peacekeepers should patrol the two countries' international border, where Russian forces, mercenaries, and materiel are routinely shipped in and out. The Russians, however, have pushed for peacekeepers to monitor the unofficial cease-fire line near the cities of Donetsk and Luhansk, and suggested changing how violations are logged and reported.
Critics of Russian actions in Ukraine, including former U.S. Ambassador to Kyiv Steven Pifer, have warned that Moscow's peacekeeping proposals appeared aimed at maintaining a "frozen conflict," similar to unresolved disputes in other parts of the former Soviet Union where a lack of resolution gives Moscow leverage over the region.
Trump has been publicly cautious in his statements on Ukraine, though he appointed veteran diplomat Kurt Volker as a special representative for resolving the crisis, and Volker has been blunt in his criticism of Russia's actions.
In recent weeks, U.S. officials have suggested that the White House may be close to heeding Kyiv's request for more defensive weaponry like antitank missiles.
The Kremlin is openly scornful of Trump's predecessor, Barack Obama. Before and after Trump's election, Moscow made no secret of its hopes that a Trump administration would be less antagonistic and more conciliatory. That included the return of two diplomatic compounds that had been ordered seized by Obama in December in retaliation for Russia's alleged meddling in last year's election.
Those hopes have been dashed -- or at least put on hold -- as the Trump administration has continued its refusal to return the compounds. Congress added its heft by passing new sanctions legislation to further punish Russia, over the White House's objections.
Moscow eventually responded by ordering a sharp cut in U.S. diplomatic staffing in Russia, which was followed by similar moves by Washington, including the outright closure of the Russian consulate in San Francisco.
Adding further to the tensions are suspicions that have hung over Trump regarding his associates' contacts with Russian officials before and after the U.S. election.
Aside from the criminal indictments of former campaign manager Paul Manafort and a business partner, a guilty plea by former foreign policy adviser George Papadopoulos, and other indictments said to be expected soon, congressional investigators have been scrutinizing a salacious report compiled by a former British spy on Trump known as the Steele Dossier.
They've also been digging into Russian-controlled social-media accounts on Facebook and Twitter that appear to have sought to influence Americans on hot-button social issues and topics that arose during the campaign.
Russian officials have appeared eager to deflect attention from the allegations of interference in internal U.S. politics, instead blaming holdovers from the Obama administration for a poisonous bilateral atmosphere. Russian Foreign Minister Sergei Lavrov echoed that approach in remarks shown on state-run TV this week, predicting that any agreement the two might reach would be undermined by "political infighting."
"They will immediately become an element of internal political fighting, internal political games aimed at making President Trump's life and activities as difficult as possible," he said.