Twenty-two people have been killed and 59 injured after suspected suicide bomber 22-year-old Salman Abedi detonated a home-made device at the end of a concert by US singer Ariana Grande at Manchester Arena.
Here is what we know so far.
Police say a lone male suicide bomber detonated a home-made bomb in the foyer of Manchester Arena as crowds were leaving the concert on Monday evening.
Twenty-two people were killed in the explosion, including an eight-year-old girl.
A further 59 people, including 12 under the age of 16, were injured and taken to hospital.
The attacker died at the scene.
Eyewitnesses said the noise of the explosion was followed by a flash of fire.
Metal nuts and bolts were strewn around the floor among bodies and the smell of explosives was in the air, witnesses said.
More than 240 emergency calls were made; 60 ambulances and 400 police officers attended.
After the attack hundreds of people in Manchester took to social media to offer spare beds and rooms for those stranded in the city.
Who carried out the attack?
Salman Abedi, 22, has been named by police as the suspected suicide bomber.
Abedi was born in Manchester on New Year’s Eve 1994, the BBC understands.
It is thought that he has at least three siblings: an elder brother who was born in London, and a younger brother and sister who were born in Manchester.
The family, believed to be of Libyan origin, has lived at several addresses in Manchester, including at a property at Elsmore Road in the Fallowfield area, that was raided by police on Tuesday.
Salford University said Abedi had been a student there, but gave no further details.
The so-called Islamic State group has claimed responsibility, but this has not been verified.
Investigators are trying to establish whether Abedi was acting alone, Mrs May said on Tuesday evening.
She said it was “a possibility we cannot ignore” that there was a “wider group of individuals linked to this attack”, and said the UK’s international terrorism threat level had been raised to “critical”.
A 23-year-old man was arrested in connection with the attack on Tuesday morning, and police executed warrants in two areas of Manchester: one in Whalley Range and another in Fallowfield, where a controlled explosion took place.
Officers are working with the National Counter Terrorism Policing Network and the intelligence services to try to establish more details about the attacker.
GMP chief constable Ian Hopkins said it was the “most horrific incident” Greater Manchester has faced.
Anyone with information can call the anti-terror hotline on 0800 789321.
The police have also appealed to anyone with images or footage from last night that they believe could assist in the investigations to upload it to ukpoliceimageappeal.co.uk or ukpoliceimageappeal.com
Some victims named
Student Georgina Callander was the first of those who were killed to be named. She was studying health and social care at Runshaw College in Lancashire.
Eight-year-old Saffie Rose Roussos, from Leyland, Lancashire, was killed.
And the third victim has been named as John Atkinson, 28, of Radcliffe in Bury.
A further 19 people who died have not yet been named.
The injured are being treated at eight hospitals in Greater Manchester.
Many have life-threatening conditions, the prime minister said.
A hotline has been set up for people concerned about loved ones – on 0800 096 0095.
A help centre for anyone needing assistance has also been set up at Gate 11 of Manchester City’s Etihad Stadium.
Relatives are using social media to hunt for missing loved ones.
Thousands of people attended a vigil in Albert Square, in central Manchester, on Tuesday evening.
What disruption has been caused?
A cordon remains in place around Manchester Arena and Victoria station while forensic work is carried out.
All train services to and from Victoria station were cancelled and the station will remain closed on Wednesday.
It could be “several days before it reopens”, rail operator Northern’s regional director, Liam Sumpter, said.
A joint statement says that it will be up to schools to decide whether exams should go ahead.
Take That have postponed their Tuesday night Liverpool concert as a mark of respect, as well as their homecoming dates this Thursday, Friday and Saturday, at Manchester Arena.
As a result of the decision to raise the terror threat level – the first time it has been “critical” since 2007 – members of the armed forces will replace armed police at certain “key sites”, Mrs May said.
The military could also be used at concerts and sporting events.
Extra armed police officers will be deployed on Saturday at Wembley for football’s FA Cup Final and at Twickenham for rugby union’s Aviva Premiership final, Scotland Yard has said.
Sporting events and venues in England say they are conducting major security reviews.