Who is affected?
Citizens of Iran, Iraq, Libya, Syria, Somalia, Sudan and Yemen are barred from entering the United States for 90 days.
After a number of twists and turns over recent days, the very latest advice from the UK Foreign Office is that people with British passports will not be affected, if they are travelling with a US visa.
That includes Britons with dual citizenship of one of the seven countries, even if they are flying to the US from that country, the Foreign Office told us on Monday afternoon.
And people who have indefinite leave to remain in the UK and hold nationality of one of the seven countries are eligible to apply for US visas.
A small number of people with the special visas granted to diplomats and their families and people who work for the UN, Nato and foreign governments are also exempt, as per the executive order signed by President Trump on Saturday.
Syrian refugees are barred from the US indefinitely, while refugees from other countries will be prevented from entering for 120 days.
What if you have a green card?
White House Chief of Staff Reince Priebus initially said those who hold green cards (people who were not born in the US but who are eligible to live and work there) would be affected by the temporary ban.
But just minutes later in a separate interview, he said “of course they were [exempt]”.
John Kelly, Homeland Security Secretary, issued a statement saying: “Lawful permanent resident status will be a dispositive factor in our case-by-case determinations.”
A White House official said on Sunday that more than 170 green card holders were allowed in on that day.
Is it a “Muslim ban”?
Not really. The executive order makes no mention of checking the religion of people attempting to enter the US.
But all seven countries are Muslim-majority, and Trump repeatedly expressed the desire specifically to halt Muslim immigration while on the presidential campaign trail.
In December 2015 he announced: “Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States.”
Now the President seems unhappy that the US media are referring to this policy as a “Muslim ban”, although it’s not clear how often this phrase has been used in reporting.
The New York Times used the words in an editorial piece. Some other news organisations have used the phrase in inverted commas, and others have referred to “predominantly Muslim” or “mostly Muslim” countries.
Trump advisor and lawyer Rudy Giuliani told Fox News the President had used the phrase “Muslim ban” and approached Giuliani on advice on how to enact it.
Giuliani said: “When [Trump] first announced it he said: ‘Muslim ban’. He called me up. He said: ‘Put a commission together. Show me the right way to do it legally.’
While Trump’s executive order doesn’t single out Muslims, it does say that when the refugee programme resumes, priority should be given to claims “made by individuals on the basis of religious-based persecution, provided that the religion of the individual is a minority religion in the individual’s country of nationality”.
This suggests that Iraqi Christians might end up getting priority over Iraqi Muslim refugees, and recent tweets from Trump suggests he has the plight of Middle Eastern Christians on his mind.
Things don’t look too hopeful for Syrian Christians though, as all refugees from that country are barred from entering America until further notice.
CNN reported the case of one Syrian Christian family who flew back to Qatar after apparently being turned back at Philadelphia.
Why these countries?
The Obama administration had already placed some restrictions on certain travellers who had visited these seven countries, based on an increased risk from “foreign terrorist fighters”.
In most of the countries, there is an active ongoing conflict involving at least one major terrorist organisation. The US State Department designates Iran, Sudan and Syria as state sponsors of terrorism.
Some critics have questioned why other countries with a stronger historical connection to terror attacks on US targets have not been included.
Of the 19 men who killed around 3,000 people in the September 11, 2001, terror attacks, 15 were from Saudi Arabia and the others from the United Arab Emirates, Egypt and Lebanon.
Some commentators have pointed out that the Trump Organization has business interest in Saudi Arabia and other Muslim-majority countries.
White House Chief of Staff Reince Priebus said on Sunday that Trump’s business activities did not influence the list of countries and more countries might be added to the list in subsequent executive orders.
According to a new report from Duke University, 23 per cent of Muslim Americans involved with violent extremist plots since 9/11 had family backgrounds in these seven countries. But none of them carried out attacks that caused fatalities.
Indeed, according to New America’s terror database, every one of the 12 terrorists who has killed anyone in the United States since 9/11 has been a US citizen or legal resident.
None of them emigrated from, or came from a family that emigrated from, one of the seven countries on the Trump list.
Is Islamic terrorism a major threat?
This point is arguable, but there are statistics available that enable us to get some measure of the danger posed by Islamic extremism in the US, in the context of other threats.
The Duke study finds that 123 people have been killed by Muslim American extremists since the September 11 attacks, 54 of them in 2016.
Last year 188 people were killed in mass shootings in America carried out by non-Muslims. The total death toll for gun crime in 2016 was around 15,000 people.
How will the ban play with voters?
It’s too early to say. Opinion polls carried out before the new travel restrictions were put in place suggest a majority of Americans backed the idea of immigration restrictions on terror-prone regions, but most were unhappy about singling out Muslims.
We don’t know if the events of recent days will have changed people’s opinions.
(UPDATE: Rasmussen Polls has this survey of 1,000 likely voters, carried out on January 25 and 26, which shows 57 per cent supported the temporary ban, 33 per cent opposed and 10 per cent were undivided.)
What do US politicians say?
At time of writing, some 60 senators are known to oppose the restrictions (46 Democrats and 12 republicans) and just four (all Republicans) support it, while 37 have remained silent on the issue (36 Republicans and one Democrat).
Only one governor has publicly supported President Trump’s order – Alabama’s Robert Bentley, a Republican – while 15 say they are opposed (5 Republicans, 10 Democrats) and 35 remain silent (27 Republicans, 7 Democrats, 1 independent).