Ten days before he was even sworn into office in 2017 Donald Trump was tweeting about the political “witch hunt” against him – and since then the phrase has appeared in more than 150 other tweets.

As for “Russia”, that has appeared more than 300 times since the president was elected. The vast majority of mentions related to what has become special counsel Robert Mueller’s investigation into Russian election meddling and possible collusion with the Trump campaign.

The Mueller probe has been a constant presence around Mr Trump’s White House, and after two years in office it has never been closer to the president. From former associates appearing in court, to current officials testifying to Congress, the drip-drip of details about the investigation continues.

Unlike in other areas of his presidency, Mr Trump has been consistent in stating that has been “no collusion” between his administration and Moscow. But as investigators continue to nibble away at his former inner circle – five former Trump advisors are among the more than 30 people who have indicted or pleaded guilty to crimes – the scope of the investigation expands.

Take Mr Trump’s former lawyer Michael Cohen for instance. Last year he pleaded guilty to financial crimes and campaign finance violations relating to hush money payments to two women, adult actress Stormy Daniels and Playboy model Karen McDougal, who have claimed affairs with the president. Mr Trump has denied the accusations of affairs, but Cohen has claimed he was working at the behest of the president over those payments – something the White House has also denied.

That financial case was passed to New York federal prosecutors by Mr Mueller’s team, with Cohen later pleading guilty to another charge from the special counsel of lying to Congress about a Trump building project in Moscow. Cohen is due to start a three-year prison sentence over the charges in March, but will publicly testify to Congress about his work for the president on 7 February.

Another two stories this week have come out around Cohen. He has acknowledged paying an IT firm to try and manipulate online polls in 2014 and 2015 in favour of Mr Trump. Again, he has claimed it was at “the direction” of the president. A second, and seemingly more serious, report by Buzzfeed News alleges that Mr Trump asked Cohen to lie to Congress about the details of plans to build a Trump Tower in Moscow, a project that did not come to fruition. The report, citing two law enforcement officials, says that Mr Trump received reports from Cohen on the project at a time when the president was saying publicly he had no business ties to Russia.

Democrats in Congress have pledged to investigate the report, with Mr Trump having repeatedly denied ever asking his former lawyer to break the law. A number of Democrats have called on Trump to resign if the allegations prove to be true.

The special counsel's office has since disputed the accuracy of the story, however, in a rare on-the-record statement.

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In the main, Mr Trump has always seemed to want to take the route of letting the storms of outrage surrounding the Mueller investigation to play out around him; repeating his denials and displaying his frustration about the probe without taking further action. However, the action he has taken has been high-profile. He forced out his former attorney general Jeff Sessions after months of complaining about how he had recused himself from overseeing the Mueller probe, and fired former FBI director James Comey – who had been in charge of the federal probe – are examples of that.

As the president moves into the second half of his term, the clamour over the Mueller investigation will only grow more frenzied. Given the flurry of court cases in the last few months, including that surrounding Mr Trump’s former campaign chairman Paul Manafort, the odds are that Mr Mueller is close to wrapping up his probe. However, with the Democrats now in charge of half of Congress – having taken the majority in the House of Representatives – investigations into Mr Trump’s personal and business life will only likely increase.

Rudy Giuliani, Mr Trump’s lead lawyer dealing with the Mueller investigation and a former New York mayor, has repeatedly called for the probe to end. He had predicted in May last year that the special counsel’s investigation would end in September, so as not to risk affecting the midterm elections.

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In a sign that Mr Trump will face more strife from the Mueller investigation during his next two years in office, Mr Giuliani – who has become known for his contradictory statements to the press – suggested earlier this week that he “never said there was no collusion” between the Trump campaign and Russia, claiming only that Mr Trump himself was not involved in collusion.

Before the latest Cohen reports were published on Thursday, Mr Giuliani attempted to clarify his comments, saying that he had “no knowledge” of collusion taking place.

All of this adds up to the fact that Mr Trump will have to be ready for Mr Mueller’s investigation to hang like an albatross around his neck for some time yet. Even if the special counsel does submit his report soon, there will likely be arguments about how much will be made public. Mr Trump’s latest pick for attorney general to replace Mr Sessions – William Barr – spent much of his confirmation hearings this week assuring the Senate that as much of the report as possible would be put into the public domain. And that Mr Mueller would be able to finish his work unencumbered.

Then there are the Democrat-led committees in the House who will no doubt try to arrange as many hearings as possible around the issues raised by the Mueller investigation.