And Mueller's interest in Russian contacts may extend to Trump's business, as well, with the special counsel's office recently asking for records related to a failed 2015 proposal for a Moscow Trump Tower, according to a person familiar with the request.
A key question in the investigation - and one that hangs over Trump's presidency - is whether these instances add up to a concerted Russian Government effort to probe and infiltrate the Trump campaign, or whether they were isolated coincidences and, therefore, inconsequential.
Ultimately, Mueller must decide whether anyone in Trump's orbit coordinated with the Russians, and, if so, if such actions were illegal or just unseemly. Collusion itself is not a crime.
The new court filings, along with recent interviews and other documents reviewed by the Washington Post, reveal more details than were previously known about the extent to which Trump's campaign became a magnet for people who believed US policy towards Russia should be retooled - and for Russians who agreed.
In all, documents and interviews show there are at least nine Trump associates who had contacts with Russians during the campaign or presidential transition.
Some are well-known, and others, such as Papadopoulos, have been more on the periphery.
Trump's one-time campaign chairman, Paul Manafort, had extensive ties to Russian business interests, remained in close touch with a Russian colleague, and discussed holding private campaign briefings for a Russian businessman close to Russian President Vladimir Putin.
A top Trump Organisation lawyer, Michael Cohen, corresponded through intermediaries with Moscow property developers about trying to build a Trump Tower there.
Donald Trump jnr's meeting with the Russian lawyer at Trump Tower in New York came after promises that the Russians had dirt on Hillary Clinton they wanted to share with the Trump campaign.
Trump's son-in-law, Jared Kushner, was also at that meeting, as well as a December encounter with Russia's ambassador in which Kushner suggested setting up a secret communications channel between the Trump transition team and the Kremlin.
Papadopoulos repeatedly tried to work with Russians to set up a meeting between Trump and Putin. Page travelled to Moscow during the campaign. Another foreign policy adviser, J.D. Gordon, met the Russian ambassador on the sidelines of the Republican National Convention.
The Russian ambassador also met twice with then-Senator Jeff Sessions, now Trump's Attorney-General, and discussed sanctions with Trump's incoming national security adviser, Michael Flynn, during the presidential transition - a conversation that later led to Flynn's resignation.
Russian government officials have rejected the notion that any contacts with Trump's campaign or business were directed by the Government or part of any effort to interfere with the US presidential election.
Trump in the past denied that he or his associates communicated with Russia during the campaign. Now, he and his allies are seeking to minimise the importance of the contacts that have emerged.
"I think the American public can fully appreciate that those are isolated, obviously disconnected events, quite small in number for a presidential campaign," said Ty Cobb, a White House lawyer. "Nothing about the actual facts published to date suggests that the president while he was a candidate ever met a Russian, ever spoke to a Russian, or colluded with anybody."
Experts who have studied Russian tactics see something different: a picture emerging of a concerted and multi-faceted Kremlin effort to infiltrate Trump's campaign.
"You've got some consistency here in terms of the Russian tradecraft . . . The general pattern of Russians appearing to try to find soft spots, to find the soft underbelly of the campaign to make contact," said Steve Hall, who retired from the CIA in 2015 after 30 years running and managing Russia operations. "I just think there's way too much smoke out there for there to be absolutely no fire."
Even if there was fire from the Russian side, it remains unclear how those within the Trump campaign reacted.
In the case of Papadopoulos, new court filings show he shared his contacts with the Russians in at least one meeting with Trump and Sessions and other times with Trump's campaign manager and lower level staffers.
At times, according to emails described to the Post, he was rebuffed. But in one August 2016 email exchange cited by prosecutors, national campaign co-chairman Sam Clovis encouraged Papadopoulos to meet with Russian officials, writing, "Make the trip, if it is feasible".
The release of the Papadopoulos guilty plea came amid a dramatic week in Washington that underscored the potential peril for Trump and his inner circle and revealed more details of Russia's apparent efforts to meddle in the US election in multiple ways.
Facebook and other social media companies provided more details about how their platforms were manipulated through what outside researchers have said was a sophisticated campaign to mimic American political conversation with the intention of shaping the behaviour of US voters - and in some cases by remotely organising political rallies in American cities.
Facebook, for instance, acknowledged that on its platform alone, posts created by Russian operatives may have been seen by as many as 126 million users. That's in addition to 11 million potentially reached by Russian-bought Facebook ads, and 20 million by posts on Instagram, which Facebook owns. Facebook has said it is working to improve the security of its platform.
The use of social media came in addition to elements of the Russian operation that were identified months ago by the US intelligence community - including the hacking of emails from the Democratic National Committee and Democratic officials that were spread during the campaign's final months via WikiLeaks.
The first sign that Russians might have been interested in connecting with Trump came soon after his June 2015 announcement that he was running for president.
At a town hall meeting in Las Vegas the following month, a young Russian gun rights activist named Maria Butina found her way to a microphone and asked the Republican candidate to describe his foreign policy, "especially in the relations with my country".
Trump promised that if elected he would improve relations. "I know Putin and I'll tell you what, we get along with Putin," Trump said.
Butina, who did not respond to requests for comment last week, told the Post in April that her question to Trump was "happenstance" and that she has never been an employee of the Russian Government.
As the campaign progressed, Trump broke with the scepticism of Moscow embraced by the foreign policy establishment in both parties. He consistently expressed admiration for Putin, questioned long-held assumptions about future support for Nato and the value of sanctions against Russia for its invasion of Crimea.
Some with long personal and business ties to Russia practically elbowed their way into the campaign.
Longtime Republican operative Paul Manafort had not been involved in a US political campaign for years until he tracked down one of Trump's oldest friends, Thomas Barrack, not long after Trump lost the Iowa caucuses and asked to be connected.
"Paul came to me and said, 'I really need to get to [Trump], I think I can be really effective at the convention,' " Barrack said in a recent interview.
He was hired in March 2016 and named campaign chairman two months later.
Manafort, who was charged last week as part of Mueller's probe with money laundering, making false statements and failing to register as a foreign lobbyist, had worked for Russia-friendly politicians in Ukraine and had in the past undertaken multimillion-dollar business deals with Russian aluminium magnate Oleg Deripaska.
Manafort pleaded not guilty, and his lawyer told reporters that the charges were "ridiculous".
During his five months working for the Trump campaign, he had repeated contact with a Russian employee of his Kiev office, including two in-person meetings.
The assistant, Konstantin Kilimnik, is a Russian Army veteran who has told associates he used to work with Russian military intelligence. Kilimnik, in a statement earlier this year to the Post, denied intelligence ties.
Over email, Manafort asked Kilimnik to pass a message to Deripaska, offering "private briefings" about Trump's campaign. Manafort's spokesman has said the emails represented an "innocuous" effort to collect past debts, and he had envisioned "routine" briefings for Deripaska. A spokeswoman for Deripaska has said he never received the message and that no briefings were held.
In court papers released last week, prosecutors said Manafort and a "Russian national who is a long-standing employee" of Manafort's lobbying firm served as "beneficial owners and signatories" on bank accounts that Manafort used to shift money around the world. The description matches Kilimnik. They also said his company has employees in both Ukraine and Moscow and noted his "connections to Ukrainian and Russian oligarchs".
One of Trump's campaign foreign policy advisers, Carter Page, had lived and worked in Moscow and produced a trail of writings proposing repairing relations between the United States and Russia.
Like Manafort, Page volunteered himself to the campaign, snagging an introduction from New York Republican chairman Ed Cox. Cox, who told the Post in May that Page had reached out to him in early 2016 asking to be connected to the Trump campaign, described Page as "very informed and up to date on things".
Trump announced Page's role in March 2016, and in July, Page travelled to Moscow and spoke at a Russian university.
Other than briefly greeting a deputy minister who attended his speech, Page has denied government contacts on the trip and said scrutiny of him is the result of Democratic persecution for his pro-Trump views. Page answered questions last week before the House Intelligence Committee, which is expected to release a transcript in the coming days.
Papadopoulos too appears to have volunteered himself, first to the campaign of another Republican presidential candidate, Ben Carson, and later to Trump's team.
Court documents show that he had repeated contacts with a Russian woman and a man with ties to Russia's Foreign Ministry, starting days after he was named a Trump adviser in March 2016 and extending for months.
In April, he was told by a London-based professor that the Russians had dirt on Clinton, including thousands of her emails.
Other Russia contacts came through more established members of Trump's world.
Cohen, a lawyer for the Trump Organisation and a close confidante of the President, fielded two requests during the campaign from Russians interested in building a Trump Tower in Moscow.
Cohen quickly declined one that arrived in late 2015, a proposal submitted through an intermediary on behalf of a billionaire Russian property developer.
But Cohen was engaged on the other Russian tower proposal, which came from Moscow developer Andrei Rozov and has recently drawn Mueller's attention. That plan had come to Cohen through a friend, a Russian-American former Trump business partner named Felix Sater, who Cohen has said encouraged him to make visits to Russia.
Trump signed a letter of intent to further explore the proposal with Rozov's company in October 2015.
Rozov has not responded to requests for comment.
Sater has acknowledged the effort, saying it was "abandoned" by the Trump Organisation. Sater's lawyer, Robert Wolf, declined to comment.
Cohen has said that he never visited Russia and that the tower plan, which was cancelled in January 2016, was "simply one of many development opportunities" the Trump Organisation has fielded over the years. His lawyer declined to comment.
Meanwhile, Russia's ambassador to the United States, Sergey Kislyak, was seeking to reach out to Trump's circle.
After attending a foreign policy address from the rising candidate in April 2016, where he briefly greeted Trump and was seated in the front row, Kislyak then met at an event on the sidelines of Republican National Convention with Trump aides Page and Gordon. The ambassador met at another event with Sessions.
Sessions met Kislyak in his Capitol Hill office in September. Sessions has said he accepted the meeting in his role as a senator rather than as a representative of the campaign.
The Kislyak meeting with Kushner during the presidential transition, in which the two discussed setting up the secret communications channel, has also drawn the interest of investigators. The Post reported this year that Kushner suggested using Russian diplomatic facilities in an apparent effort to protect their discussions from monitoring, and that Kislyak reported the idea to his superiors in Moscow, according to intercepts of Russian communications that were reviewed by US officials.
Mueller's team is also probing the Trump Tower meeting held by Trump jnr and the Russian lawyer, interviewing one of the participants before a grand jury in August.
Trump jnr has said he believes the Russian lawyer sought the gathering under false pretenses, that she shared no information about Clinton and that he had no further communication with her or her representatives.
But it was not Trump jnr's only interaction with people tied to Moscow during the campaign.
A top Russian central bank official and former lawmaker, Alexander Torshin, told Bloomberg that he sat with Trump jnr at a National Rifle Association dinner in the northern spring of 2016, though a White House official has said the two exchanged only a brief greeting.
Then, in October, just weeks before the election, Trump jnr delivered a paid speech in Paris to the Centre of Political and Foreign Affairs, a French think-tank that advocates the Russian position on some foreign policy issues.
Randa Kassis, a founder of the group, told the Post that she went to Moscow shortly after the November election and briefed Russian deputy foreign minister Mikhail Bogdanov on the speech.
Trump jnr's speech in Paris was first reported by the Wall Street Journal. Alan Futerfas, a lawyer for Trump jnr, declined to comment.
Some potential contacts with Russians are not fully understood.
The United Arab Emirates arranged a secret meeting shortly before Trump's inauguration between Blackwater founder Erik Prince and a Russian close to Putin as part of an apparent effort to establish a back-channel line of communication between Moscow and the president-elect, US, European and Arab officials told the Post earlier this year.
Prince had no formal role with the Trump campaign or transition team, and a Prince spokesman that the meeting "had nothing to do with President Trump". But officials told the Post that Prince presented himself as an unofficial envoy for Trump to high-ranking Emiratis involved in setting up his meeting with the Putin confidant.
Butina, the woman who had first questioned Trump about Russia after he became a candidate, reappeared later in the campaign.
She was part of a group that sought a meeting with the campaign in June 2016 to discuss the persecution of Christians around the world, according to Rick Clay, a politically connected former Iraq war contractor who conveyed the request to the campaign. Clay said Trump adviser Rick Dearborn turned down the request, which was first reported by CNN.
"They made the right call," Clay said.
