That ends our coverage of the first day of the impeachment trial of President Donald Trump - only the third such trial in US history.

So far the senators have debated the rules under which the trial should be conducted. No witnesses have yet been authorised to testify.

Despite efforts by Democrats to force the White House to provide documents, the vote failed after splitting along party lines.

This is just the beginning, of course. Republican Senate leader Mitch McConnell, who sets the rules for the chamber, says he is hoping the trial will last just 10 days.

Follow the latest on the day's historic events here:

Trump trial starts with rule wrangling in the Senate

A constitutional lawyer dissects the Trump defence team's argument here:

Analysis: 'No crime, no impeachment' is a shaky defence

Image source, Getty Images

Florida Congresswoman Val Demings, one of the Democratic impeachment managers, has just become the first black person to speak on the Senate floor during an impeachment trial.

"No president in history has ever done anything like this," she told senators.

"I have never seen anyone take such extreme steps to hide evidence allegedly proving his innocence," the former Orlando police chief added.

Presidential impeachments get all the attention, but they are not the only ones who can be impeached.

Impeachment is a process that holds any senior public official to account.

Other notable figures who have been impeached, external include William Blount, a Tennessee senator, in 1797 "on charges of conspiring to assist in Great Britain’s attempt to seize Spanish-controlled territories in modern-day Florida and Louisiana".

The House of Representatives has impeached 15 judges since 1803, according to the US Federal Judicial Centre, external. However, only two have been

The most recent was in 2010, when a federal judge in Louisiana was found guilty of perjury and removed by the Senate.

And Richard Nixon's vice-president Spiro Agnew once asked the House to launch an impeachment investigation into himself, external, but they refused.

Lead Democratic impeachment manager Adam Schiff raised eyebrows when he used a crude term on the Senate floor today.

The California congressman said: "When you hear them attack the House managers, what you’re really hearing is... we don’t want to talk about how - to pardon the French expression - ass-backwards it is to have a trial and then ask for witnesses."

That comment left journalists pondering if that the first time this vulgarity was heard in the hallowed chamber.

Nope.

As the congressional record shows, Senator Lindsey Graham, a South Carolina Republican, said it twice in 2016.

Jonathan Turley, professor of constitutional law at George Washington University, writes:

Forty-five years ago, Cowboys quarterback Roger Stauback said: "I closed my eyes and said a Hail Mary."

The so-called Hail Mary pass is now a mainstay of American football where a quarterback, in the final seconds of a close game, throws the ball into the end zone on a hope and a prayer.

As the NFL play-offs wrap up and the Senate impeachment trial begins, Stauback's strategy came to mind. The White House has decided to frame its defence around a constitutional Hail Mary pass in arguing that the impeachment itself is invalid because articles of impeachment must be based on alleged criminal acts.

The "quarterback" in this play is Harvard Professor Alan Dershowitz who believes that the Senate should simply dismiss the case as constitutionally invalid. Hail Mary passes make for great football but perfectly lousy impeachment trials.

The problem is that this pass is not going into the constitutional end zone but well beyond the stadium. The argument is based on a literal reading of the standard "high crimes and misdemeanours".

Those are criminal terms, to be sure, but they were never viewed as such in England, where the standard was first forged, nor in the United States in past judicial and presidential impeachments.

Jonathan Turley testified with other constitutional experts in both the Clinton and Trump impeachment hearings.

Read his full article

Image source, Getty Images

After his first rules change amendment failed in a party line vote, Senator Chuck Schumer asks that State Department documents and records be subpoenaed by Chief Justice John Roberts.

It remains to be seen whether any witnesses will be allowed to testify during the Senate trial of Donald Trump.

By a party-line vote of 53-47, Democrat Chuck Schumer's proposed rules amendment has failed.

He had asked that Chief Justice John Roberts subpoena White House Chief of Staff Mick Mulvaney to turn over documents related to Trump's phone call with the leader of Ukraine.

CBS News, the BBC's US affiliate, has shared details from inside the Senate chamber.

Republican senators have been quite friendly with White House counsel, CBS reports. They have been shaking hands, offering smiles and pats on the back.

While Democratic House intelligence committee chairman Adam Schiff was in full prosecutor mode, CBS says Trump lawyer Jay Sekulow was more in full Fox News guest mode, speaking loudly in defence of the president.

When the White House counsel addressed Schiff, the Democrat stared back, inscrutable. Democratic Senate leader Chuck Schumer, meanwhile, often wore a mocking smile.

Bernie Sanders, a Democratic presidential hopeful, was seen with his hand in front of his face the whole time.

Some Republicans were seen passing notes or whispering to each other.

When the White House counsel mentioned the presidential candidates and how they would rather be in Iowa campaigning ahead of the first votes, Sanders' brow furrowed and his 2020 rival Elizabeth Warren gave the attorney a glare.

Former Republican National Committee Chairman Michael Steele has tweeted that Trump's lawyer, Pat Cipollone, is arguing before an audience of one - Trump himself.

The BBC's Anthony Zurcher reminds us that Trump wanted a made-for-TV lawyer to defend him.

Image source, Getty Images

California Democratic Congresswoman Zoe Lofgren has just become the first woman to present arguments as an impeachment manager in any presidential impeachment in US history.

The impeachments of Andrew Johnson and Bill Clinton featured only male impeachment managers.

This is her third impeachment process. Back in 1974 she worked for the House Judiciary Commitee where she drafted articles of impeachment against Richard Nixon.

President Trump's lawyer Alan Dershowitz decried his client's impeachment over the weekend because, he said, there was no crime committed.

Impeachment calls for a standard of "high crimes and misdemeanors" - a much debated phrase that dates back to the Constitution and doesn't necessarily mean the law has been broken.

A central plank in Trump's defence is that impeachment should only be applied to allegations of criminal conduct.

But, in 1998, Mr Dershowitz seemed to make the opposite argument in a CNN interview.

Anthony Zurcher
BBC North America reporter

Q: If the Senate are (almost certainly) not going to vote to impeach Trump, then what is the point in this whole process? - Will Fox, Leeds

A: If you listen to Democrats, the reason they're going through with this even though the outlook is slim to none for Senate conviction is because they feel obligated to hold the president accountable for his actions.

They view the president as having abused his power by pressuring Ukraine to open investigations into a political rival, and if they don't draw the line here - even if it doesn't result in his removal - the president will be emboldened to take further actions that could adversely affect Democrats in the 2020 election.

Then there's the purely political fact that the Democratic base have been howling for impeachment for months.

If Democratic officeholders hadn't taken action, they would have risked the ire of their most loyal supporters - and either faced primary challenges or lost general elections because their side didn't feel sufficiently motivated to turn out at the polls.

Anthony has answered more of your questions on the trial here.

Democratic leader Chuck Schumer has introduced an amendment to his Republican counterpart's resolution.

He's asking for the ability to subpoena White House documents related to the Ukraine matter.

Democratic members of the House of Representatives are acting as prosecutors in this trial. Two will be more prominent than the rest.

Adam Schiff is a 59-year-old is chairman of the House intelligence committee and has already become a figurehead of the investigation. A former LA prosecutor, he gained his seat in Congress in 1998 and was appointed to the intelligence committee a decade later.

He’s been a frequent target of the president, whose mocking nicknames for him include “Liddle Adam” and “Shifty Schiff”.

Mr Schiff said he was "humbled" by his appointment as lead prosecutor. Admirers see him as the man with extensive knowledge of the impeachment case, best suited to present it to the Senate.

Another key figure is Congressman Jerry Nadler - the head of the House Judiciary Committee.

The 72-year-old has served as a congressman for New York since 1992, and has a reputation as a passionate defender of civil liberties with a very liberal voting record.

Jason Crow, Val Demings, Hakeem Jeffries, Zoe Lofgren and Sylvia Garcia are the other House impeachment managers for the trial.

Image source, Drew Angerer/Getty Images

In his opening statement, Democratic House manager Schiff decried what he called Trump's "dangerous nonsense", accusing the president of acting against America's national security.

He added to the chorus of Democrats criticising the trial rules, asking: "How would you structure the trial if you didn't know what your party was?"

Schiff, who is the lead Democrat impeachment manager, said most Americans "don't believe that the Senate will be impartial", while calling on Senators to act as proper jurors.

He played several clips of the president in which Trump said he: could do anything he wanted because of the Constitution; would be fine having officials testify in the trial; that he will fight subpoenas.

"In the name of national security, [Trump] would hide graphic evidence of his dangerous misconduct," Schiff says. "The only question is ... will you let him?"

Schiff also noted that in the past three Senate impeachment trials (including of judges), new witnesses were allowed. He said adding new witnesses was a "definitive tradition...when trying articles of impeachment".

He wrapped up by saying "the truth will come out".

"The question is, will it come out in time?" he said.

President Donald Trump addressed the impeachment trial directly on Tuesday for the first time since proceedings began.

"READ THE TRANSCRIPTS!" was his Twitter dispatch from Switzerland, where the president is attending the World Economic Forum in Davos.

He has tweeted "read the transcript" 37 times since September.

The transcript in this case refers to a read out of his 25 July call with Ukrainian President Volodmyr Zelensky. What was intended by Trump in that call is the heart of the impeachment scandal.

Earlier in the day, before arguments had begun on the Senate floor, Trump told reporters at the mountainside resort that the forthcoming trial was a "hoax" and a "witch hunt going on for years".

For the president, the trial might be far out of sight, but clearly not out of mind.

Image source, US Senate

One tradition of bipartisanship that has survived the impeachment is the Senate candy desk, which legend has it has been stocked full of sweets since 1965.

The desk, full to the brim of various sweets, is currently operated by Pennsylvania Republican Pat Toomey. It's a place for senators, includes those working long hours during rare impeachment trials, to grab a quick unhealthy snack. It is located near the entrance most frequently used by Republicans.

During the trial of Bill Clinton, the impartiality of Pennsylvania Republican Rick Santorum was questioned after it was found that candy was only being offered to Republicans.

"My response was, ‘Touche,'" Santorum told The Morning Call, external newspaper in a recent interview.

"So we immediately got candy to the Clinton defenders, and made sure that they were well-stocked for the rest of the trial. You have to be impartial when it comes to candy."

The drawer drew attention last week as senators were being sworn in as jurors. Utah Republican Mitt Romney was seen by cameras pointing out the desk to the chamber's newest member, Kelly Loeffler of Georgia.

Anthony Zurcher
BBC North America reporter

Image source, Chip Somodevilla/Getty Images

Mitch McConnell made some last-minute changes to his proposal for how the Senate will conduct Donald Trump’s impeachment trial. The House managers and the president’s defence team now have three days each, instead of two, to present their opening arguments (although each side’s total time is still capped at 24 hours).

He has also changed the rules of evidence somewhat, allowing the House managers to introduce material gathered during their hearings unless a majority of the Senate objects.

McConnell has said he had the Republican votes he needed to pass his rules package, but perhaps he felt some pressure from within his own ranks to more closely align his proposal to the way Bill Clinton’s impeachment trial was run in 1998.

Democrats will still be calling for more, however. They want a guarantee of witnesses, something that doesn’t seem likely to happen.

Image source, Getty Images

No pictures or filming are allowed inside the chamber, apart from a single feed from C-Span. But according to CBS News, the BBC's US partner, the atmosphere inside today is focused, almost tense.

Many senators, on both sides, have been seen taking extensive notes, including Republicans Thom Tillis and Rob Portman, and Democrats Amy Klobuchar and Michael Bennet (both 2020 presidential hopefuls).

When the White House counsel presented his brief statement, lead impeachment manager Adam Schiff watched him carefully, attentively, with no overt emotion.

The Democrat House managers and House counsel have been interacting, according to CBS, but there is little talking between the White House counsel.

When Schiff played a soundbite of the president during his remarks, Democratic Senate leader Chuck Schumer appeared to have a smirk on his face.