The Mueller special counsel investigation was started by Deputy Attorney General Rod Rosenstein, who was serving as Acting Attorney General due to the recusal of Attorney General Jeff Sessions. He authorized Robert Mueller to investigate and prosecute "any links and/or coordination between the Russian government and individuals associated with the campaign of President Donald Trump", as well as "any matters that arose or may arise directly from the investigation" and any other matters within the scope of 28 CFR 600.4 – Jurisdiction.

The investigation's broad scope allowed Mueller to investigate many topics, including: Russian election interference; links between Trump associates and Russian officials; alleged collusion between Trump campaign and Russian agents; potential obstruction of justice; financial investigations; lobbyists; Trump as a subject of investigation; other topics; and the Facebook–Cambridge Analytica data scandal.

Russian election interference

In late-July 2016, the FBI opened counterintelligence investigations into four Americans who had contact with Trump to determine whether they might have coordinated or cooperated with Russia's activities. Those investigations became part of the Special Counsel's portfolio.

Among the U.S. intelligence agencies, the Federal Bureau of Investigation and the Central Intelligence Agencies in January 2017 concluded "with high confidence" (and the National Security Agency with "moderate confidence") that the Russian government interfered in the election by hacking into the computer servers of the Democratic National Committee (DNC) and the personal Gmail account of Clinton campaign chairman John Podesta and forwarding their contents to WikiLeaks, as well as by disseminating fake news promoted on social media, and by penetrating, or trying to penetrate, the election systems and databases of multiple U.S. states. de Volkskrant reported on January 25, 2018, that Dutch intelligence agency AIVD had penetrated the Russian hacking group Cozy Bear in 2014 and in 2015 observed them hack the State Department and White House in real time, as well as capturing the images of the hackers via a security camera in their workspace. The New York Times reported on July 18, 2018, that American, British and Dutch intelligence services had observed stolen DNC emails on Russian military intelligence networks. NBC News reported on March 1, 2018, that Mueller was assembling a case for criminal charges against Russians who carried out the hacking and leaking. Those charges were brought on July 13, 2018.

Russia's influence on U.S. voters through social media is a primary focus of the Mueller investigation. Mueller used a search warrant to obtain detailed information about Russian ad purchases on Facebook. According to a former federal prosecutor, the warrant means that a judge was convinced that foreigners had illegally contributed to influencing a US election via Facebook Ads.

On February 13, 2018, in testimony before the Senate Intelligence Committee, the heads of the top six American intelligence agencies unanimously reaffirmed Russian interference. Three sources familiar with Trump's thinking told CNN he remains unconvinced that Russia interfered because it suggests he didn't win the election solely on his own merits.

During a July 16, 2018, press conference at the 2018 Russia–United States Summit in Helsinki, Finland, President Putin was asked, "did you want President Trump to win the election and did you direct any of your officials to help him do that?" Putin replied, "Yes, I did. Yes, I did. Because he talked about bringing the US-Russia relationship back to normal."

The Mueller Report concluded while there was no evidence that the Trump campaign conspired with Russia to influence the election, the Russian government did attempt to influence the election in Trump's favor by hacking Democratic political organizations and spreading "disinformation and social media" discord.

Links between Trump associates and Russian officials

As early as spring 2015, American intelligence agencies started overhearing conversations in which Russian government officials, some within the Kremlin, discussed associates of Trump, then a presidential candidate.

The New York Times reported on February 14, 2017, that phone records and communications intercepts showed that Trump associates—including members of the Trump campaign—had "repeated contacts" with senior Russian intelligence officials during the 2016 campaign. Paul Manafort was the only Trump associate who was specifically identified as participating in these communications. In addition, some senior Trump associates, including Kushner, Trump Jr., Sessions, Flynn and Manafort, had direct contacts with Russian officials during 2016. In congressional testimony the following June, Comey stated the Times report was "in the main" not true. The Times reported that during the intervening months, its sources continued to believe the reporting was "solid." In July 2020, the Senate Judiciary Committee released notes taken contemporaneously with the Times report by FBI Counterintelligence Division chief Peter Strzok indicating his skepticiam about the Times''' reporting, writing, “We have not seen evidence of any officials associated with the Trump team in contact with [intelligence officers]" and "“We are unaware of ANY Trump advisors engaging in conversations with Russian intelligence officials.” The Times stood by its account, subsequently reporting that the released notes did not provide a fully accurate representation of Strzok's knowledge. Michael Flynn was forced to resign as National Security Advisor on February 13, 2017, after it was revealed that on December 29, 2016, the day that Obama announced sanctions against Russia, Flynn had discussed the sanctions with Russian ambassador Kislyak. Flynn had earlier acknowledged speaking to Kislyak but denied discussing the sanctions. Also in December 2016, Flynn and presidential advisor Jared Kushner met with Kislyak hoping to set up a direct, secure line of communication with Russian officials about which American intelligence agencies would be unaware. Jared Kushner also met with Sergei Gorkov, the head of the Russian state-owned bank Vnesheconombank (VEB), which has been subject to U.S. economic sanctions since July 2014. Flynn and Kushner failed to report these meetings on their security clearance forms.

The Trump Organization pursued a luxury hotel and condominium project in Moscow—dubbed the Trump Tower Moscow—during the Trump presidential campaign. This project was facilitated by Michael Cohen, then an attorney for the Trump Organization, and from January 2017 to May 2018 Trump's personal attorney. Trump signed a nonbinding "letter of intent" dated October 13, 2015, to proceed with the project. The letter, also signed by Russian investor Andrei Rozov, was forwarded to Cohen by Russian-American real estate developer Felix Sater, who had worked with The Trump Organization on prior deals, including Trump SoHo and Trump International Hotel & Residence. Sater has also been involved in criminal activities involving organized crime and has served as an informant to the FBI relating to those activities. He boasted to Cohen about his connections to Vladimir Putin, saying in an email to Cohen on November 13, 2015, "Buddy our boy can become president of the USA and we can engineer it. I will get all of Putins [sic] team to buy in on this. I will manage this process." He also asserted that he had secured financing for the project through the Russian state-owned VTB Bank, which was under sanctions by the United States government. Cohen emailed Putin spokesman Dmitry Peskov in January 2016 to request assistance in advancing the project and later stated he didn't recall receiving a response. Cohen told the Senate Intelligence Committee in September 2017 that the deal was abandoned in January 2016, but in November 2018 admitted in a guilty plea that he had minimized Trump's role in the plans "to be consistent with [Trump's] political messaging" and that negotiations had actually extended through June 2016. Cohen also admitted that Peskov's office had, in fact, replied to his January 2016 email and discussed the deal with him on the phone. In a sentencing memorandum filed the day after his guilty plea, Cohen's attorneys stated he kept Trump "apprised" of the "substantive conversation" Cohen had with the Russian official, and discussed with Trump traveling to Russia to advance the project during the summer of 2016. BuzzFeed News reported on March 12, 2018, that Mueller's investigators had questioned Sater, and on April 13, 2018, reported that a former Russian spy had helped secure financing for the project. In 2010, Sater was provided business cards describing himself as "Senior Advisor to Donald Trump" with an email address at TrumpOrg.com. In a 2013 sworn affidavit, Trump said "If [Sater] were sitting in the room right now, I really wouldn't know what he looked like," and in 2015 he stated "Felix Sater, boy, I have to even think about it. I'm not that familiar with him."

The Trump team issued multiple denials of any contacts between Trump associates and Russia, but in sixteen cases those denials turned out to be false. On December 4, 2017, in a court filing requesting that the judge revoke Manafort's bond agreement, prosecutors stated that Paul Manafort had worked with a Russian intelligence official to draft an op-ed essay while he was out on bail.The New York Times reported, on March 28, 2018, that former Trump campaign deputy chairman Rick Gates had, in September and October 2016, frequently communicated with a man that the FBI believes is a former agent of GRU, Russia's largest foreign intelligence agency, and who had maintained active links with Russian intelligence during these communications; this disclosure was written into a court sentencing document for Alex van der Zwaan, submitted by Robert Mueller. Identified in the document as "Person A", The Times reported that the man matched the description of Konstantin Kilimnik, who, for years, was Paul Manafort's "right-hand man" in Ukraine. Gates reportedly told an associate that he knew "Person A" was a former GRU agent, although Manafort told associates he was not aware of such a connection. The Times reported on January 8, 2019, that in spring 2016 Gates and Manafort gave polling data, some of which was private to the Trump campaign, to Kilimnik, asking he pass it to Ukrainians Serhiy Lyovochkin and Rinat Akhmetov. During a closed-door court hearing on February 4, 2019, regarding false statements Manafort had made to investigators about his communications with Kilimnik, special counsel prosecutor Andrew Weissmann told judge Amy Berman Jackson that "This goes, I think, very much to the heart of what the special counsel's office is investigating," suggesting that Mueller's office continued to examine a possible agreement between Russia and the Trump campaign.

Reuters reported on March 29, 2018, that the special counsel is examining an event at the 2016 Republican National Convention at which Jeff Sessions had conversations with Russian ambassador Sergei Kislyak. Investigators are also looking into how and why language deemed hostile to Russia was removed from the Republican party's platform document during the convention. Mueller's office is also inquiring whether Sessions had private conversations with Kislyak at a Trump speech at the Mayflower Hotel in April 2016.