Donald Trump may have hoped for a quiet Christmas after another tumultuous year in the White House.

Yet the US government has been forced into a state of partial shutdown after Mr Trump insisted he would not sign a spending bill without $5 billion for the border wall. The president also faces criticism from Republicans over his decision to pull US troops from Syria and the recent resignation of Defence Secretary Jim Mattis.

Most crucially of all for Mr Trump, the investigation by special counsel Robert Mueller and related criminal probes show no sign of easing up.

What are the investigations all about?

Mr Trump is facing criminal investigations in both Washington and New York. The special counsel is looking into whether the Trump campaign coordinated with Russia and whether the president obstructed the investigation.

The president also plays a central role in a separate case in New York, where prosecutors have implicated him in a crime. They say Mr Trump directed his personal lawyer Michael Cohen to make illegal hush money payments to two women as a way to quash potential sex scandals during the campaign.

Where does the Mueller probe stand now?

The president’s pick for attorney general, William Barr, sent an unsolicited memo to the Justice Department this year criticising parts of the Mueller probe as “fatally misconceived”.

The 20-page memo, sent in June while Mr Barr was in private practice and months before he was selected by Mr Trump for the Justice Department job, may prompt questions about his ability to oversee the special counsel’s investigation fairly.

The document argues that there could be disastrous consequences for the Justice Department and the presidency if Mr Mueller were to conclude that acts a president is legally permitted to take –such as firing an FBI director – could constitute obstruction of justice, just because someone concludes that there was corrupt intent.

Who could be running against Trump in 2020? Show all 23 1 /23 Who could be running against Trump in 2020? Who could be running against Trump in 2020? Joe Biden The former vice president - poised to be a frontrunner - has announced his run. He recently faced scrutiny for inappropriate touching of women, but was thought to deal with the criticism well AFP/Getty Who could be running against Trump in 2020? Bernie Sanders The 2016 runner-up has announced that he will be running again in 2020 Getty Who could be running against Trump in 2020? Hillary Clinton The 2016 Democratic presidential candidate and former Secretary of State says she is “still considering” whether she will run again. Getty Who could be running against Trump in 2020? Pete Buttigieg The Indiana mayor and war veteran will be running for president. If elected, he would be the first openly LGBT+ president in American history. Getty Who could be running against Trump in 2020? Kamala Harris The former California attorney general will be running for president in 2020. Introduced to the national stage during Jeff Sessions’ testimony, she has endorsed Medicare-for-all and proposed a major tax-credit for the middle class. AP Who could be running against Trump in 2020? Elizabeth Warren The Massachusetts Senator has formally launched her bid for president in 2020. A progressive Democrat, she is a major supporter of regulating Wall Street. AP Who could be running against Trump in 2020? Beto O’Rourke The former Texas congressman told Oprah Winfrey that he “has been thinking about running for presidency”, but stopped short of formally announcing his bid to run in 2020. AFP/Getty Who could be running against Trump in 2020? Wayne Messam Mayor of the city of Miramar in the Miami metropolitan area, Wayne Messam has announced his bid. He intends to run on a progressive platform against the "broken" federal government. He favours gun regulations and was a signatory to a letter from some 400 mayors condemning President Trump's withdrawal from the Paris Climate Accord. Vice News Who could be running against Trump in 2020? Kirsten Gillibrand The New York Senator formally announced her presidential bid in January, saying that “healthcare should be a right, not a privilege.” Getty Who could be running against Trump in 2020? Cory Booker The New Jersey Senator has announced that he will be running for the presidency in 2020. If he secures the nomination he said finding a female vice president would be a priority. Getty Who could be running against Trump in 2020? John Delaney The Maryland congressman was the first to launch his bid for presidency, making the announcement in 2017. AP Who could be running against Trump in 2020? Julian Castro The former San Antonio mayor announced his candidacy in January and said that his running has a “special meaning” for the Latino community in the US. Getty Who could be running against Trump in 2020? Tulsi Gabbard The Hawaii congresswoman announced her candidacy in January, but is likely to face tough questions on her past comments on LGBT+ rights and her stance on Syrian President Bashar al-Assad. Getty Who could be running against Trump in 2020? Andrew Yang The entrepreneur has announced his presidential candidacy, and has pledged that he would introduce a universal basic income of $1,000 a month to every American over the age of 18. AFP/Getty Who could be running against Trump in 2020? Marianne Williamson The author and spiritual advisor has announced her intention to run for president. She had previously run for congress as an independent in 2014 but was unsuccessful. Getty Who could be running against Trump in 2020? John Kerry The former secretary of state has said he is still thinking about whether to run. Getty Who could be running against Trump in 2020? Michael Bloomberg The entrepreneur and former New York mayor– with a net worth of around $50bn – has said he will decide by the end of February whether to seek the presidency. AFP Who could be running against Trump in 2020? Howard Schultz Former Starbucks CEO Howard Schultz has not yet ruled out running for president in 2020, despite criticism that his bid could help re-elect Mr Trump by dividing the Democrat vote. AP Who could be running against Trump in 2020? Eric Holder The former attorney general has said he will decide in “the next month or so” whether to run as a 2020 presidential candidate. AP Who could be running against Trump in 2020? Eric Swalwell The California congressman said he is “ready to do this” and will decide before April whether to run. MSNBC Who could be running against Trump in 2020? Terry McAuliffe The former Virginia governor, who worked to elect Democratic governors during 2018 midterms, said there was a “50 per cent” chance he would run. AP Who could be running against Trump in 2020? Sherrod Brown The Ohio senator is still undecided about whether to run for president in 2020. Who could be running against Trump in 2020? Mitch Landrieu The former New Orleans mayor said he doesn’t think he will run for president, but “never say never”. AP Photo/Jacquelyn Martin

Did the Trump campaign collude with Russia?

There is no smoking gun when it comes to the question of Russia collusion. But the evidence so far shows a broad range of Trump associates had Russia-related contacts during the 2016 presidential campaign and transition period, and that several lied about the communication.

There is also evidence that some people in the president’s orbit were discussing a possible email dump from WikiLeaks before it occurred. American intelligence agencies and Mr Mueller have said Russia was the source of hacked material released by WikiLeaks during the campaign that was damaging to Clinton’s presidential effort.

What about the possible obstruction of justice?

That is another unresolved question that Mr Mueller is pursuing. Investigators have examined key episodes such as Mr Trump’s firing of former FBI Director James Comey and his fury over the recusal from the investigation of former Attorney General Jeff Sessions.

Support free-thinking journalism and attend Independent events

What does Mr Trump have to say about all this?

The president has repeatedly slammed the Mueller probe as a “witch hunt” and insisted there was “NO COLLUSION” with Russia. He also says his now-former lawyer, Cohen, lied to get a lighter sentence in New York.

Mr Trump has reportedly become increasingly worried about the prospect of being impeached in recent days, despite his public declarations.

“It’s hard to impeach somebody who hasn’t done anything wrong and who’s created the greatest economy in the history of our country,” Mr Trump told Reuters earlier this month. “I’m not concerned, no. I think that the people would revolt if that happened.”