The impeachment trial centres around Donald Trump's objection to the election results.

When Congress met last month to certify the results, Trump had over 100 Republican lawmakers backing him up and objecting to Joe Biden's victory.

But in 2017 when Trump had just won the presidential race, the shoe was on the other foot, with a handful of Democrats objecting to certifying the results.

Trump lawyer Michael Van der Veen earlier shared a montage of some of these lawmakers, including lead impeachment manager Jamie Raskin.

Here's how Biden - who was then vice-president and presided over certifying the results - reacted when faced with those objections:

Schoen is now accusing House impeachment managers of doctoring the footage they presented to the Senate earlier this week, and of "misrepresenting tweets".

He shows a series of tweets he claims have been "manipulated" by the prosecution team, and a video clip of Trump's 6 January speech that he alleges was purposefully edited.

"Words matter, they told you," he says. "But they selectively edited the president's words over and over."

Here's our analysis of what Trump said in his 6 January speech.

Now up is David Schoen, another of Trump's lawyers.

He previously represented ex-Trump advisor Roger Stone, who was pardoned by the former president in December.

Schoen says the Democrats wanted to "rush this impeachment through the House", and points out that Trump's first impeachment hearing last year was given more consideration.

"Here, President Trump and his counsel were given no opportunity to review evidence or question its propriety," Schoen argues. "This rush to judgement is just one example of the denial of due process."

"Constitutional cancel culture" is how Trump attorney Michael Van der Veen is describing this trial of his client.

He says Trump has been "entirely consistent in his opposition to mob violence" whereas the Democrats who oppose him decide whether to endorse or condemn violence based "upon the mob's political views".

He argues that on 6 January Trump called for "peacefully and patriotically" marching to the Capitol. Telling his supporters they needed to "fight like hell" was simply political speech, Van der Veen says.

In their arguments earlier this week, Democratic impeachment managers referred to this line in Trump's address, calling it an example of incitement.

Make no mistake, Van der Veen adds, "this is an effort to smear, censor and cancel not just President Trump, but the 75 million Americans who voted for him".

Read more:

• Cancel culture: What unites young people against Obama and Trump

Van der Veen next compares the Capitol riots with protests by the Black Lives Matter movement last year.

"As many will recall, last summer the White House was faced with violent rioters night after night... culminating in the clearing of Lafayette Square."

He cites negative coverage of police and security action against protesters then - and suggests there's a link between the "political pressure" on security forces after that, and security failings on 6 January.

Last summer's protests came after the killing of George Floyd by police in Minneapolis last May.

Following the Capitol riot, many Black Americans called out double standards in how police used force to quell peaceful Black Lives Matter protests but appeared to hesitate when facing insurrection by a largely white pro-Trump mob.

Michael van der Veen, one of the lawyers representing Trump in this trial, is giving his opening remarks to the Senate.

He's so far called the impeachment trial a "politically motivated witch hunt" and has said it's "completely divorced from the facts".

As well as arguing that Trump's speech did not call for violence from supporters, Van der Veen says his challenge to the election result was lawful too.

"In the past, numerous other candidates for president have used many of the same processes to pursue their own election challenges," he adds - before showing a montage of clips from 2017 when Democrats objected to the election results that gave Trump his victory.

Michael van der Veen says there's evidence that the riots on 6 January were "pre-planned".

"Tragically, as we know now, on 6 January a small group who came to engage in violent and menacing behaviour hijacked the event for their own purposes," he says.

"The fact that these attacks were premeditated demonstrates the ludicrousness of the incitement allegations against the [former] president. You can't incite what was already going to happen."

Let's break down the trial's big arguments so far.

What are Trump's lawyers going to argue?

As we heard from them on opening day, Trump's lawyers say that impeaching a president who is no longer in office is unconstitutional.

They are also expected to argue that Trump's speech at the 6 January rally was an expression of free speech - a right protected by the First Amendment (more on that in a moment). On top of that, the defence may also say none of what Trump said actually called for violence or an invasion of the Capitol; he was just frustrated about the election.

Did Democrats address this yesterday?

Yes, they did, in a "pre-buttal" at the end of their presentation.

"Incitement to violent insurrection is not protected by free speech. There is no First Amendment defence to impeachment for high crimes and misdemeanours," said lead impeachment manager Jamie Raskin, adding that such a notion was "absurd".

OK, so what does the First Amendment say?

Here's the text, as is: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances."

So yes, it does protect freedom of speech - but a letter signed by 144 constitutional lawyers , externalahead of the trial argued that this protection could apply as a defence in legal proceedings, but in an impeachment trial.

If you want to know more, check out our Reality Check team's fact-check of Trump's defence here.

The defence of Trump against impeachment is now under way. We will be explaining all the aspects of this trial - and the actors taking part - step by step. But, if you have any questions you want the answers to right away, these four pieces will help guide you.

• What is Trump accused of?

• Who are the key players?

• Did Trump's words incite a riot?
• The other impeached presidents

The fourth day of Trump's impeachment trial has now started.

Today, we're going to be hearing from the former president's defence team.

You can watch events unfold in the Senate chamber on the BBC's own livestream. Just click 'Play' in the image at the top of this page.

Warning: video evidence may contain upsetting scenes and foul language.

Image source, Reuters

Nikki Haley was US ambassador to the UN from 2017 to 2018 and one of Trump's strongest allies - but she has now spoken out against him.

"We need to acknowledge he let us down," she tells Politico in an interview published today.

"He went down a path he shouldn't have, and we shouldn't have followed him, and we shouldn't have listened to him. And we can't let that ever happen again."

This isn't the first time she's criticised Trump, however. In a speech to the Republican National Committee in the days following the Capitol riots, she said Trump was “badly wrong with his words”.

"And it wasn’t just his words," she added then. "His actions since Election Day will be judged harshly by history."

The mob of Trump supporters who stormed the Capitol on 6 January called the loyal former vice-president a traitor who should be hanged. What changed?

The BBC's Anthony Zurcher explains.

Image source, Reuters

Donald Trump isn't the only one keeping a low profile since leaving the White House.

According to CNN, since moving down to Florida Melania Trump has kept her schedule pretty relaxed.

"She goes to the spa, has lunch, goes to the spa (again) and has dinner with Donald on the patio," one person familiar with her calendar told the US broadcaster. "Rinse and repeat. Every day."

She also often has dinner with her parents, Viktor and Amalija Knavs, who live in a private suite of rooms in Mar-a-Lago for much of the year, CNN adds.

A former deputy chief of staff at Homeland Security has told the BBC she fears there could be more extremist attacks.

Elizabeth Neumann said the 6 January riot at the Capitol is "seen as a success story for white supremacists and anti-government extremists" and they are "actively recruiting what they perceive to be disheartened Trump supporters".

The impeachment trial comes down to one question: Did Donald Trump incite the insurrection of the Capitol on 6 January?

No matter what the Senate decides, the repercussions of that day tell us a frightening truth about the divided American public.

BBC Newsnight's Gabriel Gatehouse takes a closer look at the movements of far-right extremists on the day of the riot - and how the Proud Boys were already heading to the Capitol before President Trump had even spoken at his rally.

But the vast majority of those arrested for their actions on 6 January did not have affiliations to such groups before the siege.

Experts say that many more Americans have become radicalised since the election and warn that the risk of political violence could grow.

A month-long search for offenders has resulted in charges against a reported 221 people, which you can read about here.

Image source, Reuters

Today won't be the first time we're hearing from Trump's lawyers.

At the opening of the impeachment trial on Tuesday, Bruce Castor delivered an address that is now infamous.

The statement - which was 48 minutes long - appeared to lack substantive content, and reportedly left Trump himself very unhappy.

Alan Dershowitz, who defended Trump in his first impeachment trial last year, said he could not understand what Castor had been hoping to achieve.

"There is no argument. I have no idea what he's doing. I have no idea why he's saying what he's saying," the high-profile lawyer told conservative TV channel Newsmax.

Read more about Castor's address here

Image source, Reuters

With Trump's legal team suggesting that they'll only take about three to four hours to put forward their defence, prosecutors are getting ready for the next stage of the trial - a four-hour question and answer session with senators - to begin as early as this afternoon (EST).

Both sides are allotted 16 hours, with a maximum of eight hours per day, to make their case.

Prosecutors still haven't said whether or not they plan to call witnesses to support their case against Trump, but they have said that they're confident in the arguments they've made over the last two days.

"At the end of this trial, the senators will have no choice but to vote to convict and disqualify," one senior aide on the impeachment managers team told reporters.

Image source, Reuters

Trump's defence gets under way in less than an hour and representing him in the Senate will be David Schoen, a trial lawyer, and Bruce Castor, a former district attorney.

They were only drafted in just over a week before the trial started after Trump parted ways with his previous legal team.

In a statement, both attorneys said they didn't believe the push to impeach Trump was constitutional.

Castor added: "The strength of our Constitution is about to be tested like never before in our history. It is strong and resilient. A document written for the ages, and it will triumph over partisanship yet again, and always."

Schoen has previously represented Roger Stone, former adviser to Trump. Stone received a presidential pardon in December.

The lawyer also made headlines in the past for meeting with Jeffrey Epstein in his final days to discuss possible representation, and for later saying he did not believe the death of the US financier and sex offender was suicide.

Castor, a former Pennsylvania district attorney, is known for declining to prosecute Bill Cosby for sexual assault in 2005. The comedian was eventually convicted on three counts of sexual assault in a 2018 retrial of his case.

Read more about the trial's key players here.

Image source, Library of Congress

Donald Trump is the only US president to be impeached twice and only one of three to ever be impeached at all. So who were the others?

Andrew Johnson was the first in 1868. He was accused of, among other things, dismissing his secretary of war against the will of Congress. Mr Johnson had a narrow escape - the two-thirds majority in the Senate was missed by just one vote.

Bill Clinton found himself impeached on the grounds of perjury and obstruction of justice after he lied about the nature of his affair with Monica Lewinsky and then allegedly asked her to lie about it as well. When the trial reached the Senate in 1999 the vote for a conviction failed to get close to the two-thirds backing required.

Richard Nixon, the 37th US president, resigned in 1974 before he could be impeached over the Watergate scandal.

Read more here

To impeach, in this context, means to bring charges in Congress that form the basis for a trial.

The US constitution states a president "shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes or misdemeanours".

This is a political process, rather than a criminal one.

It happens in two stages. The first stage saw impeachment charges brought to the House of Representatives and passed in a vote.

Then the process headed to the Senate where Trump's trial is now taking place.

A two-thirds vote is necessary to convict Trump. This milestone has never been reached in US history.

It also looks unlikely in this case, as 17 Republican senators would have to vote to convict Trump.

Trump has already left office but, if he were convicted, the Senate could then vote to bar him from holding elected office again.