Labour's deputy leader Tom Watson reacts, saying Prime Minister Theresa May, who preceded Amber Rudd as home secretary, is responsible for the Windrush scandal.
It's sad news, MP Damian Green tweets about his party colleague.
His prior tweet, two days ago, was in support of her as the scandal intensified.
Damage limitation?
Ms Rudd's resignation came as officials could not guarantee further damaging information would not surface, says the BBC's political editor Laura Kuenssberg.
Ms Rudd's resignation will upset a very delicate balance in the cabinet over Brexit, as the now former home secretary was a powerful "Remain" voice, political editor Laura Kuenssberg continues.
Rudd right to resign - Abbott
The shadow home secretary Diane Abbott, from the opposition Labour party, has told the BBC that Ms Rudd's decision to resign was the right one.
The timing of Ms Rudd's resignation is a surprise, the BBC political editor Laura Kuenssberg has told the BBC news channel.
She says the Home Office and No. 10 had been trying to keep Ms Rudd in her position, but it seems that in a few past hours the situation reached a tipping point.
The authorities were alerted after the Barbados government raised concerns with the Foreign Office.
Labour had been urging Ms Rudd to quit over the Windrush saga.
Who will be the next home secretary?
The odds are already being published.
Sajid Javid, currently the housing and communities secretary and formerly the business secretary, is currently the favourite at Ladbrokes Politics.
Who are the "Windrush generation"?
Those arriving in the UK between 1948 and 1971 from Caribbean countries have been labelled the Windrush generation.
Many of the arrivals became manual workers, cleaners, drivers and nurses - and some broke new ground in representing black Britons in society.
The Home Office did not keep a record of those granted leave to remain or issue any paperwork confirming it - meaning it is difficult for Windrush arrivals to prove they are in the UK legally.
But those who lack documents are now being told they need evidence to continue working, get treatment from the NHS - or even to remain in the UK.
Earlier this month, Amber Rudd apologised for their treatment, saying it was "wrong" and "appalling".
There has been dispute over whether or not there were removal targets for immigrants, and if the Ms Rudd was aware of them.
On Sunday, the Guardian published a letter from the home secretary to PM Theresa May, in which Ms Rudd had set out her "ambitious but deliverable" aim to deport 10% more illegal immigrants over the "next few years".
Ms Rudd telephoned the prime minister on Sunday evening to tell her of the decision amid intensifying opposition demands for her to quit.
A No 10 spokesman said: "The Prime Minister has tonight accepted the resignation of the Home Secretary."
Windrush backlash
She was under pressure over the Windrush scandal. Some migrants from Commonwealth Caribbean countries, who settled in the UK from the late 1940s to the 1970s, had been declared illegal immigrants. In some cases they and their relatives were threatened with deportation, lost their jobs, or were refused access to medical treatment.
BreakingRudd resigns
UK Home Secretary Amber Rudd had been expected to make a statement in the House of Commons on Monday, but on Sunday evening she resigned.
Live Reporting
Paul Gribben, Francesca Gillett and Claire Heald
All times stated are UK
PM Theresa May 'should be next', opponents tweet
Labour's deputy leader Tom Watson reacts, saying Prime Minister Theresa May, who preceded Amber Rudd as home secretary, is responsible for the Windrush scandal.
His party colleagues Dawn Butler and Emma Dent Coad agreed.
Support for the idea that Theresa May should go comes from the Scottish National Party benches too.
Rudd is "decent, clever and conscientious"
It's sad news, MP Damian Green tweets about his party colleague.
His prior tweet, two days ago, was in support of her as the scandal intensified.
Damage limitation?
Ms Rudd's resignation came as officials could not guarantee further damaging information would not surface, says the BBC's political editor Laura Kuenssberg.
PM 'regretfully' accepted Ms Rudd's resignation
What really pushed Ms Rudd were documents about migration targets, the BBC's political correspondent Iain Watson tells the BBC News channel.
He says Downing Street would have preferred her to stay, adding that he was told that the Prime Minister regretfully accepted her resignation.
Ms Rudd didn't want to go - but felt she had no other choice, our correspondent says.
Morning announcement
The BBC's Political Editor Laura Kuenssberg says Ms Rudd's replacement will be announced in the morning.
'Proud of my sister'
Ms Rudd's brother has tweeted a show of support.
(He is the chairman of Open Britain, an organisation that campaigns "against a hard, destructive Brexit".)
Cabinet balance on Brexit will be lost
Ms Rudd's resignation will upset a very delicate balance in the cabinet over Brexit, as the now former home secretary was a powerful "Remain" voice, political editor Laura Kuenssberg continues.
Rudd right to resign - Abbott
The shadow home secretary Diane Abbott, from the opposition Labour party, has told the BBC that Ms Rudd's decision to resign was the right one.
Timing of resignation - a surprise
The timing of Ms Rudd's resignation is a surprise, the BBC political editor Laura Kuenssberg has told the BBC news channel.
She says the Home Office and No. 10 had been trying to keep Ms Rudd in her position, but it seems that in a few past hours the situation reached a tipping point.
Authorities 'were alerted back in 2016'
The Home Office and Downing Street had been told in 2016 about problems faced by the Windrush generation, the BBC reported earlier this week.
The authorities were alerted after the Barbados government raised concerns with the Foreign Office.
Labour had been urging Ms Rudd to quit over the Windrush saga.
Who will be the next home secretary?
The odds are already being published.
Sajid Javid, currently the housing and communities secretary and formerly the business secretary, is currently the favourite at Ladbrokes Politics.
Who are the "Windrush generation"?
Those arriving in the UK between 1948 and 1971 from Caribbean countries have been labelled the Windrush generation.
Many of the arrivals became manual workers, cleaners, drivers and nurses - and some broke new ground in representing black Britons in society.
The Home Office did not keep a record of those granted leave to remain or issue any paperwork confirming it - meaning it is difficult for Windrush arrivals to prove they are in the UK legally.
But those who lack documents are now being told they need evidence to continue working, get treatment from the NHS - or even to remain in the UK.
Earlier this month, Amber Rudd apologised for their treatment, saying it was "wrong" and "appalling".
Read more here.
Ms Rudd's letter to Theresa May
There has been dispute over whether or not there were removal targets for immigrants, and if the Ms Rudd was aware of them.
On Sunday, the Guardian published a letter from the home secretary to PM Theresa May, in which Ms Rudd had set out her "ambitious but deliverable" aim to deport 10% more illegal immigrants over the "next few years".
Ms Rudd telephoned the prime minister on Sunday evening to tell her of the decision amid intensifying opposition demands for her to quit.
A No 10 spokesman said: "The Prime Minister has tonight accepted the resignation of the Home Secretary."
Windrush backlash
She was under pressure over the Windrush scandal. Some migrants from Commonwealth Caribbean countries, who settled in the UK from the late 1940s to the 1970s, had been declared illegal immigrants. In some cases they and their relatives were threatened with deportation, lost their jobs, or were refused access to medical treatment.
BreakingRudd resigns
UK Home Secretary Amber Rudd had been expected to make a statement in the House of Commons on Monday, but on Sunday evening she resigned.