Former customs officers say policing the post-Brexit border will be a mammoth task.Read more
A Conservative MP is hoping to increase pressure on Commons Speaker John Bercow by tabling a no-confidence motion.
Mr Bercow said this week he would be "strongly opposed" to US President Donald Trump addressing Parliament, accusing him of "racism and sexism".
James Duddridge said Mr Bercow had "overstepped the mark" although he did not expect his motion to be debated.
Meanwhile an early day motion calling for officials to withhold permission for Mr Trump to address Parliament, has now been signed by 204 MPs - largely from the Labour Party.
Here's a reminder of the main stories so far today
Labour MPs named in Jeremy Corbyn's new frontbench line up were all elected in the 2015 election.
So what else is known about the relative newbies...?
Shadow business secretary Rebecca Long-Bailey, MP for Salford and Eccles, was born in Greater Manchester to Irish parents. She studied politics and sociology at Manchester Metropolitan University. She backed Jeremy Corbyn for the leadership in 2015 and 2016.
Shadow environment secretary Sue Hayman, MP for Workington, became the first woman MP in Cumbria. She is originally from Berkshire and previously stood for Labour in Preseli Pembrokeshire in 2005, Halesowen and Rowley Regis in 2010 – narrowly losing in both. She backed Yvette Cooper for the Labour leadership in 2015, but didn't nominate in 2016.
Shadow Welsh secretary Christina Rees, MP for Neath,was a shadow justice minister in January 2016 but resigned after the EU referendum, only to return to the job in October 2016. She backed Andy Burnham for the Labour leadership in 2015 and Owen Smith in 2016.
Shadow chief secretary to the Treasury Peter Dowd, MP for Bootle, became a Merseyside councillor in 1981, was elected to Sefton Council in 1991, becoming leader in 2008. He led Sefton’s first ever Labour controlled council from May 2013. He is related to former Labour MPs Simon and Peter Mahon. He backed Andy Burnham for the Labour leaderhip in 2015, but didn’t nominate in 2016.
Jeremy Corbyn also named Sue Hayman as shadow environment secretary, promoting her from the shadow minister role in the same department.
Labour's Christina Rees is the new shadow Wales secretary and Peter Dowd takes over as shadow chief secretary to the Treasury.
Mr Corbyn commented:
I’m pleased to announce appointments to Labour’s shadow cabinet. We have a wealth of talent in our party and the strength of our shadow team will develop Labour’s alternative plan to rebuild and transform Britain, so that no one and no community is left behind.”
Jeremy Corbyn has promoted Salford and Eccles MP Rebecca Long-Bailey to replace Clive Lewis, who quit as shadow business secretary to vote against the Brexit Bill.
Sporting a hard hat, Jeremy Corbyn took a break from debate over Brexit and questions over his leadership to visit an affordable housing development in Ashton-under-Lyne, Greater Manchester.
Apple boss Tim Cook has told Theresa May the technology giant is "very optimistic" about the UK's future after Brexit.
Mr Cook met the prime minister at Downing Street this morning and referenced the company's plans to build a new UK headquarters at the redeveloped Battersea Power Station as proof of the company's support of the UK.
We're doubling down on a huge headquarters in the Battersea area and we're leaving significant space there to expand. We're a big believer in the UK - we think you'll be just fine. Yes, there will be bumps in the road along the way but the UK's going to be fine."
Last year the iPhone maker revealed it would move 1,600 employees to the new campus in south London in 2021.
In a statement about the meeting, Apple said: "Tim had a positive meeting with the prime minister today, discussing Apple's continued investment in the United Kingdom.
"We are proud that Apple's innovation and growth now supports nearly 300,000 jobs across the UK."
According to the Financial Times, Rupert Murdoch was in the room when Donald Trump gave his first post-election foreign newspaper interview, to former cabinet minister and Times columnist Michael Gove.
The chairman of News Corp did not feature in photographs of the encounter last month at the top of Trump Tower in Manhattan but two people have confirmed he was in the room, the paper says.
The interview was conducted by Mr Gove, a leading proponent of the UK’s exit from the EU.
The FT says Mr Murdoch’s presence is a sign of the mogul’s interest in Mr Trump and his close relationship with the new president and his family.
Metropolitan Police Commissioner Sir Bernard Hogan-Howe says his officers "have just got to get on with" handling the security surrounding US President Donald Trump's state visit, despite having less notice than normal for such an event.
The trip could reportedly take place in June.
Sir Bernard tells LBC radio that police usually got "about six months' notice" to work on such events.
He says: "At the moment, of course, people are concerned that there might be lots of protests - there have been already.
"So no doubt as the days pass we will make assessments for what is going to happen."
Work and Pensions Committee chairman Frank Field has welcomed the Insolvency Service's decision to appoint "specialist counsel and forensic accountancy services to analyse the evidence they have gathered on the sale and collapse of BHS".
The Labour MP has been highly critical of Arcadia chairman Sir Philip Green since the group sold BHS for £1 in 2015.
He said: "It seems the net is tightening around the former directors of BHS." Mr Field added that his committee and the Forfeiture Committee - which has the power to remove honours, including knighthoods - "will await the outcome of their investigations with great interest”.
MPs voted in October that Sir Philip should lose his knighthood - but this has no legal force.
BHS collapsed with the loss of 11,000 jobs and carrying a £571m pension deficit.
Sir Philip has vowed to sort out the pension problem.
The RMT union has announced it is to ballot members working on Arriva Rail North over strike action.
The dispute focuses on the role of guards on the company's services.
The RMT has been involved in industrial action on Southern trains for several months.
Shrewsbury's Polish-born MP Daniel Kawczynski says he is sure the rights of European citizens living in the UK will be secured during the Brexit negotiations.
He said he supported "the rights of Poles in the UK, just as I support the rights of Brits in the EU" and that he believed in the prime minister's Brexit strategy.
Mr Kawczynski also criticised an amendment put forward which called for the rights of all EU citizens in the UK to be protected.
He said it would have weakened the British hand, ahead of any negotiations.
Sixteen "unlawfully elected" councillors are still active in Tower Hamlets the London Assembly has heard.
Tower Hamlets' Mayor, John Biggs, said councillors linked to his disgraced predecessor Lutfur Rahman were "drawing expenses and participating in decisions".
He told the London Assembly's Police and Crime Committee that: "if the party they were elected under was an improper organization then something further should have happened."
In April 2015 an Electoral Court Judge removed Mr Rahman from office after he was found guilty of electoral fraud and declared the previous election void.
Foreign Secretary Boris Johnson, who was born in New York, has given up his American citizenship.
The Conservative announced he planned to hand back his US passport while he was London mayor and began the process more than a year ago.
US government documents listing people who have given up their citizenship rights confirmed he no longer had the status.
During a trade mission to America in 2015, Mr Johnson described his dual nationality as "an accident of birth" that he planned to change, but said the process was "a laborious business".
US laws mean that American citizens are liable to pay some taxes even if they are not resident in the country.
Mr Johnson was forced to settle an "outrageous" capital gains tax bill following the sale of a house in London ahead of his US mayoral tour.
The previous year he had insisted he would not settle up, saying: "Why should I? I haven't lived in the United States for, you know, well, since I was five years old."
During the joint press conference in Downing Street, Theresa May is pressed on whether there should be a second Scottish referendum.
The UK PM side-steps the question but reiterates that the Scottish people had voted to remain in the UK during the 2014 poll and the SNP had described that occasion as a "once in a generation vote".
Mrs May stresses that the UK is intensifying its discussions with the Scottish government and other devolved administrations to get the "best possible deal" for the whole of the UK to trade with and operate in the European market.
House of Commons
There has been "disgusting incitement" by the Palestinians, says Conservative Philip Hollobone.
However, he adds that language used by Jewish settlers has been "equally vile".
We are never going to find resolution until we deal with both sides of the argument, he argues.
He asks "what can we do other than shouting from the touchlines".
He says he is not in favour of boycotting Israeli products but wants the government to adopt "a robust method of action against Israeli government".
The Italian prime minister Paolo Gentiloni says the UK's decision to leave the EU did not fill the Italians with joy - but it is one they respected..
Speaking at a joint press conference with UK Prime Minister Theresa May, he stresses that there is no point in the EU having a destructive relationship with the UK.
He argues that while the negotiations over Brexit "won't be easy...we need to show a constructive and friendly approach".
Mr Gentiloni says both leaders have a "very specific interest" to reassure Italians living in the UK and British people living in Italy that their rights will be respected post Brexit.
"From our point of view its fundamental to hear the message that ... the UK decided to leave the EU but this does not mean the country will leave Europe," he says.
House of Commons
Labour's Ian Austin accuses the motion of being one-sided and simplistic.
He says the Palestinian Authority incites violence and incentivises terrorism by paying salaries to convicted terrorists.
Furthermore, he notes that millions have been spent on promoting terrorism rather than on building schools or hospitals.
He also adds that 75% of Israeli settlers are on 6.3% of the land.
House of Commons
Joan Ryan, chair of Labour Friends of Israel, says she's opposed to the continued building of settlements which "threatens the viability of a future Palestinian state, the case for which is unarguable".
But she says that settlements are not "the only, nor the principle" barrier to peace.
She says the biggest problem is a lack of trust on both sides.
She says trust is not helped by an "unrelenting stream of anti-semitic incitement" from Palestinian authorities including children's TV programmes that teach hatred of Jews, the naming of streets after suicide bombers or announcements from state media that "all of Israel is occupied territory".
House of Commons
Foreign Affairs Committee chair Crispin Blunt says Palestinian leaders have made decisions that do not give their case the "legal and moral authority it deserves".
But, he says, we can't lose sight of the fact that "settlements are illegal under international law for a reason" and that the world has moved on from thinking you can "conquer someone's territory and colonise it".
He says that true friends of Israel should oppose their settlement policy because many people around the world see "Israel through the clouded prism of settlements".
Referencing the UK's long friendship with Israel, he says that "friends should not allow each other to make profound and damaging mistakes, which is why I support this motion".
The shadow chancellor's been talking to journalists about the Brexit bill vote and the resignation of his colleague Clive Lewis.
John McDonnell said: "It's been a tough week for us this week because a number of our people have voted to represent their constituents and I can understand that.
"But we, as the Labour Party, have to respect the referendum result and that's what we've done. The irony of it is, is that the Tories have papered over their cracks this week - if you saw George Osborne's speech he said that the fight's coming and he's going to be part of it."
He said Labour rebels would be respected because of the "difficult situation" and that Clive Lewis was "a real loss" and he was sure "he'll be back".
The shadow chancellor said that Labour would now be "uniting around our agenda" and predicted the Conservatives would split apart.
He also dismissed stories that Mr Corbyn had set a date for his departure as leader as "fake news".
Yvette Cooper says the Dubs scheme is working and the idea that the government are "pulling the plug on it" after only six months is "shameful".
The Labour MP, a former shadow home secretary, said it "goes against the spirit of Britain doing its bit .. to help the most vulnerable refugees of all".
She says there's a "bit of a stand-off" going on between Britain and France over child refugees - with the consequence that they are heading back into the arms of people traffickers.
She said hte home secretary had done some good things but she was "baffled" and "shocked" at the decision to scale down the programme.
Read more on the row here
Jeremy Corbyn tweeted "the real fight starts now" after Wednesday night's Brexit vote and it didn't go down well online.
Remain voters tweeted the phrase back at the Labour leader - but not quite in the way he may have hoped.
They added GIFs of people punching themselves in the face, Death Stars exploding, eyes rolling. That kind of thing.
Read a round-up of Twitter reaction here
BBC Radio 4
Plans to take 3,000 children fleeing from Syria have been scaled back - to 350, leading to much criticism of the government in the Commons earlier.
Conservative MP Heidi Allen told BBC Radio 4's World at One said she did not agree with the decision.
She said it was "utterly unacceptable" that the government was not prepared to go back to councils on the issue in the next financial year.
"There are an awful lot of us that are not going to let this go," she says and says she will be among MPs putting pressure on the government to reconsider.
The government says there were fears that it was encouraging people traffickers.
Here's a round-up of what's been making the headlines so far today:
BBC Radio 5 live
Labour's Chuka Umunna has clashed with former Conservative leader Iain Duncan Smith over whether an extra £350m a week will ever be spent on the NHS as a result of Brexit.
Mr Umunna was talking to Emma Barnett on BBC Radio 5 live Daily after the rejection of his amendment to the Article 50 bill, which would have forced the government to look at the impact of Brexit on NHS spending.
Mr Duncan Smith said that he voted against the amendment because he didn’t want the Article 50 bill to get dragged down with debates and legal challenges.
“This whole bill is about one thing and one thing only - this bill should not be amended in any shape or form,” he said.
He added that he hoped that the extra money will be delivered, once Brexit has happened.