A Monmouth University poll released today shows that a majority of the country thinks the trial should allow new evidence, but that support is deeply partisan.

Here are the key stats:

• 57% say the House managers should be able to present new evidence

• Support for allowing new evidence comes from 87% of Democrats, 56% of independents, and just 24% of Republicans
• More than 3 in 4 Americans say Trump and his officials should be invited to testify, but only 40% think Trump should be compelled to testify
• 53% approve of the House of Representatives decision to impeach Trump, while 46% disapprove
• 49% feel Trump should be removed while 48% say Trump should not be removed

The director of the polling institute, Patrick Murray, said: "It is interesting that solid majorities in every partisan group would like to see Trump and members of his administration at least asked to appear."

Jon Sopel
BBC North America Editor

Image source, Callaghan O'Hare/Getty Images

While impeachment envelops Washington, the subject of the trial, President Donald Trump, is nowhere near. He's celebrating American prosperity at the World Economic Forum in Switzerland. But, as BBC's Jon Sopel explains, the president will be tuning in from afar.

Donald Trump wants to project himself as a serious world statesman on the stage - talking about the economy, talking about the environment, talking about the things that matter, staying away from the dog fight in Washington.

Will he be watching closely on CNN or Fox? You bet.

The impeachment has obsessed him and he is deeply concerned about it. He wants to see what is going to happen next.

He may be 5,000 feet up a mountain, he may be seeking - literally - higher ground, but I think he'll be monitoring proceedings in DC very closely.

Republican Senator Mitt Romney of Utah, who could be a swing vote in the upcoming trial, brushed off the idea that a quicker trial, as proposed by Mitch McConnell, would be detrimental.

"Whether it's two days or four days, each side gets as much time as they did in the Clinton trial," he said, according to The Hill, external.

Republican Marsha Blackburn defended the president; Democrats Bob Casey and Kamala Harris criticised the Republican proposal as unfair.

Lead impeachment manager, Congressman Adam Schiff says the Democrat house managers "rise in opposition" to the resolution.

He begins by reiterating the charges against Trump: abuse of power, related to the president's dealings with Ukraine and obstruction of Congress.

"It is the president's apparent belief that ... he can do anything he wants, no matter how corrupt, outfitted in gaudy legal clothing," Schiff says, adding that Trump's actions are a "trifecta of constitutional misconduct justifying impeachment".

He says the obstruction charge "is every bit as destructive of our constitutional order as the misconduct charge." But, he says, the ultimate vote of whether or not to find Trump guilty is "not the most important".

"How can that be? How can any decision you make be more important than guilt or innocence, than removing the president or not removing the president? I believe the most important decision in this case is the one you will make today," Schiff says.

"Will the president and the American people get a fair trial? Will there be a fair trial?"

White House lawyer Pat Cipollone - who Trump has privately referred to as the "strong silent type" was the first to lay out the White House's defence to the Senate.

The corporate lawyer, who is a partner at America's largest firm, is leading the White House defence along with figures including Ken Starr and Alan Dershowitz.

Democrats have argued that Cipollone has first hand knowledge of Trump's alleged violations of his oath and must be compelled to testify.

Their claim that Cipollone is a "material witness" was made just hours before the Senate trial got underway.

On the Senate floor he called the argument "absolutely absurd" and said senators will ultimately find that Trump "did nothing wrong".

Pat Cipollone, White House counsel, said that the president's defence team supports the rules resolution as proposed by McConnell.

"It's time to start with this trial," Cipollone said.

"We are in favour of this [resolution]. We believe that once you hear those initial presentations the only conclusion will be that the president has done absolutely nothing wrong and that these articles of impeachment do not begin to approach the standard required by the Constitution... there is absolutely no case."

"We respectfully ask you to adopt this resolution so that we can begin with this process," he concluded. "It is long past time to start this proceeding."

Image source, Getty Images

The clerk has begun reading the rules, as proposed by Republican leader Mitch McConnell. A debate and vote will follow.

"Hear ye! Hear ye! Hear ye!" says the Senate sergeant-at-arms, who is tasked with enforcing senate rules.

"All persons are commanded to keep silent, on pain of imprisonment, while the House of Representatives is exhibiting to the Senate of the United States articles of impeachment against President Donald John Trump, President of the United States," he says.

There is a complicated story behind today's impeachment trial.

Here are your handy primers for all things impeachment.

SIMPLE GUIDE: Looking for a basic take on what's going on? This one's for you.

GO DEEPER: Here's a 100, 300 and 800-word summary of the story

WHAT'S IMPEACHMENT? It's a political process to remove a president - video guide

IMPEACHMENT QUESTIONS? We've got answers

CONTEXT: Why Ukraine matters to the US

Image source, Getty Images

Senate Republican leader Mitch McConnell's rules resolution has been met with fierce criticism from Democrats, who say it's unfair and not what he promised (which was to stick to Bill Clinton-trial rules).

Lead impeachment manager Adam Schiff said in a press conference on Tuesday morning the resolution was a "profound departure from the Clinton impeachment trial".

Here's what McConnell's resolution allows:

• Each side gets 24 hours to make opening arguments, starting Wednesday, to be completed in two days
• Senators given 16 hours to question the opposite side
• After questioning, four hours of debate to consider whether witnesses or documents should be allowed, followed by a vote

So what's different?

His plan speeds up the proceedings and does not automatically admit into evidence all the House of Representatives' findings. It also does not allow senators to introduce motions to call witnesses - they must first vote on whether to consider any new evidence at all before arguing over specific documents or witnesses.

House Republican Doug Collins, a ranking member of the judiciary committee, told Fox News the rules were "different in some ways, but you get the same basic gist".

A simple majority (51 votes) is needed to approve the rules.

The US Constitution offers little guidance on how the Senate ought to run the trial, so the game play is almost entirely in the hands of the senators.

Senate Minority Leader Chuck Schumer followed McConnell on the floor to make the Democratic case for rules that allow more witnesses to testify.

Schumer said that if Republicans were to block witness testimony, it would allow future presidents to commit "impeachable crimes with impunity".

The rules proposed by McConnell seemed to be "designed by President Trump for President Trump", Schumer said, adding that the rules would "in ways "both shameless and subtle, conceal the truth from the American people".

McConnell wanted "a trial with no existing evidence and no new evidence," Schumer added.

"A trial without evidence is not a trial. It’s a cover-up," he said.

Senate majority leader Mitch McConnell is currently speaking on the floor, defending the rules he set out ahead of the trial - which Democrats will contest when the trial gets underway at 13.00 EST.

McConnell said he would table any amendments put forward by the Democrats at the outset of the trial to call witnesses or introduce new evidence. He accused the Democrats of refusing to call witnesses when they had the chance.

"The House chose not to pursue the same witnesses they want the Senate to call," he said, adding: "No one should dictate process to United States senators."

McConnell said the trial would abide by the rules set out for the previous impeachment trial - of Bill Clinton in 1998.

"All eyes are on the Senate, the country is watching to see if we can rise to the occasion," he said.

"Twenty-one years ago, 100 senators, including some who are here today, did just that. The body approved a fair and common sense process to guide the beginning of a fair presidential impeachment trial.

"Two decades later, this Senate will retake that entrance exam. The basic structure is as fair and even handed as it was then."

Image source, Getty Images

Speaking to reporters at a bilateral meeting with European Commission president Ursula von der Leyen in Davos, Switzerland, Trump said the impeachment was "a total hoax" and a "witch hunt".

"It goes nowhere because nothing happened," he said. "The only thing we’ve done is a great job... That whole thing is a total hoax, so I’m sure it’s going to work out fine.”

White House Press Secretary Stephanie Grisham earlier said that Trump's appearance at the World Economic Forum's Davos summit was "a good chance to speak with world leaders on a variety of other topics".

"He’s the president of the United States, his work doesn’t stop because of the silliness going on in DC," she said.

Image source, Chip Somodevilla/Getty Images

Speaking to reporters hours before Trump goes on trial, Senate Minority Leader Chuck Schumer pilloried the procedure proposed by ranking Republican Mitch McConnell as "completely partisan".

"The McConnell rules seem to be designed by President Trump for President Trump," he said.

He continued: "A trial with no evidence is not a trial at all, it's a cover-up," echoing remarks by his Democratic colleagues in the House from earlier today.

"It will go down in history as one of the very dark days of the Senate."

Image source, Getty Images

John Roberts, the chief justice of the US Supreme Court, will preside over the trial. It is his job to make sure the senators stick to the rules. So who is he?

Roberts was the youngest chief justice in more than 200 years, taking the position in 2005 at the age of 50.

Born in New York and raised in Indiana, Roberts attended a boarding school as a teenager but also spent summers working in a steel mill. He considered becoming a historian at Harvard, but went to law school there instead.

He spent many years as a lawyer in the Reagan administration and then entered private practice, arguing before the high court and serving as one of several legal advisers to George W Bush in the Florida presidential recount case.

Though he is ideologically conservative, Roberts is seen as the swing vote in a court stacked with conservative-leaning justices. He has voted with the court's liberals in recent cases involving the Trump administration, including asylum policy, abortion law and a death row case. But he sided with the court's conservatives in allowing the president to enforce his policy of banning certain transgender people from the military.

Image source, FiveThirtyEight

An impeachment certainly isn't a bright spot on a presidential record, but according to President Trump's approval rating his popularity has not taken much of a hit.

FiveThirtyEight, a statistics-driven news site, has been tracking national approval polls since Trump entered office. According to their analysis, the president is sitting at 42.2% approval and 53.4% disapproval - roughly the same level he's been at since April 2018.

And even as the impeachment trial consumes Washington, Trump's popularity is not dramatically different than that of his predecessors.

On this same day in Barack Obama's presidency, Obama was just three points more popular - with a 45.1% approval and 48.8% disapproval.

And edging out both Trump and Obama, on his 1097th day in office President George W. Bush boasted a 55.1% approval rating and 40.8% disapproval.

Amid a fierce debate over the rules of the trial, both Republicans and Democrats are urging constituents to call in and share their opinions.

According to a new poll by CNN, external, 69% of Americans say new witness testimony should be allowed.

Image source, Getty Images

Speaking before the start of the Senate trial on Tuesday, Democratic House Managers Adam Schiff and Jerry Nadler spoke to the media about the rules proposed by Mitch McConnell, the most senior Republican in the Senate.

To debate whether to have witnesses and introduce new evidence was "to be debating whether you should have a cover-up," Nadler said.

"Any senator who votes to deny a witness is voting to cover-up the president's actions," he said.

Schiff echoed Nadler's remarks: "This is not the fair trial that the American people want," he said.

Most believe it's a foregone conclusion that Trump will be acquitted at the end of this process, because his party controls the Senate.

But could the trial go off script? The BBC's Anthony Zurcher and Shrai Popat take a front row seat.

Image source, Alex Wong/Getty Images

44 Democrats are expected to vote for Trump's removal.

So far, the Trump impeachment has proved an entirely political process. With more than 80% of Democrat voters supporting Trump's removal from office, Democratic senators from blue-leaning states are expected to vote for the president's removal.

3 Democrats on the fence.

Joe Manchin of West Virginia, Kyrsten Sinema of Arizona and Doug Jones of Alabama are all Democrats worth watching as Trump's trial heats up. All are from red-leaning states, and all have voted with Republicans for key votes, like the confirmation of Attorney General Bill Barr.

5 Republicans on the fence.

On the other side of the aisle, five Republicans may also buck party loyalty in their ultimate vote.

Lisa Murkowski of Alaska, Mitt Romney of Utah, Susan Collins of Maine, Cory Gardner of Colorado, and Ben Sasse of Nebraska have all - in one way or another - expressed concerns with President Trump and could break with their party.

The likelihood of them doing so will be influenced by their electoral chances. Gardner, Collins and Sass are up for re-election in 2020 and they'll need strong Republican support to ensure victory.