Twenty-two people, including children, have been killed and 59 injured in a suicide attack at Manchester Arena.
The blast happened in the foyer at 22:35 BST on Monday at the end of a concert by US singer Ariana Grande.
Police said the lone male attacker, who died in the blast, detonated a homemade bomb.
Relatives are using social media to hunt for missing loved ones, and an emergency number, 0161 856 9400, has been set up.
The prime minister has chaired a meeting of the government's emergency Cobra committee and is expected to travel to Manchester later.
Chief Constable Ian Hopkins said it was "the most horrific incident" the city had ever faced.
He said the "fast-moving investigation" was now working to establish whether the attacker "was acting alone or as part of a network".
Sixty ambulances attended the incident and those wounded are now being treated at six hospitals around the city.
Eyewitnesses described seeing metal nuts and bolts among the debris, and spoke about the fear and confusion that gripped the concertgoers.
Andy Holey, who had gone to the arena to pick up his wife and daughter, said: "An explosion went off and it threw me about 30ft from one set of doors to the other set of doors.
"When I got up I saw bodies lying on the ground. My first thought was to go into the arena to try to find my family."
Emma Johnson said she and her husband were at the arena to pick up her children, aged 15 and 17.
"We were stood at the top of the stairs and the glass exploded - it was near to where they were selling the merchandise," she told BBC Radio Manchester.
"The whole building shook. There was a blast and then a flash of fire afterwards. There were bodies everywhere."
Teenager Abigail Walker, who was at the concert, told the BBC: "I had to make sure I had my sister. I grabbed hold of her and pulled hard. Everyone was running and crying.
"We were just trying to figure where everyone was. It was absolutely terrifying."
Charlotte Campbell's daughter Olivia has been missing since the concert.
"She's only a 15-year-old girl, she's out there on her own because her friend has been found," she told the BBC.
"If anyone sees her contact me. Give her your phone and let her ring me. I just want her home."
The UK threat level has been has been judged to be severe for nearly three years - which means an attack is considered highly likely.
But in recent months the tempo of counter terrorist activity has been increasing with - on average - an arrest every day.
After the attack in Westminster by Khalid Masood in March, police and security officials have been warning that further attacks were almost inevitable.
But they also believed that those were more likely to be low-tech involving knives or vehicles. The fact that the Manchester attack involved explosives will worry them.
It may not have been at the level of complexity seen in Paris in 2015, when multiple attackers sent from Syria used guns and suicide belts, but it will still have required planning.
Police have established a help centre at Manchester City's Etihad Stadium, access Gate 11, for anyone who needs assistance in tracing loved ones.
Twitter has been flooded with appeals from relatives and friends of missing concertgoers via the hashtag #MissingInManchester.
Facebook also activated a safety check feature so that people can let their family and friends know they are safe.
The blast happened close to the entrance to Victoria railway and tram station. The station has been closed and all trains cancelled.
Police also carried out a precautionary controlled explosion in the Cathedral Garden area of the city at about 01:32. The force later confirmed it was not a dangerous item.
Greater Manchester Mayor Andy Burnham said the city would "pull together", adding: "That's what we are. That's what we do. They won't win."
The Manchester Arena or MEN is the city's largest indoor venue with a concert capacity of around 21,000.
Police are encouraging anyone with footage from the scene to upload it at ukpoliceimageappeal.co.uk or ukpoliceimageappeal.com. Other information can be reported to the anti-terrorist hotline on 0800 789 321.
Former Manchester Central MP Lucy Powell has praised the solidarity and support of the people of Manchester following the bomb attack on the Manchester Arena.
Powell told 5 live Breakfast: “The people have come together to try and support families, children that have been separated from their parents, and that is the spirit of our city and that spirit will never be killed, will never die.”
“That is the positive that we can take out of this horrific and heart-breaking attack.”
Eight-year-old Saffie Roussos and Georgina Callander, believed to be 18, are among the dead
Saffie Rose Roussos was a pupil at Tarleton Primary School, in Lancashire.
Her head teacher, Chris Upton, said she had been "simply a beautiful little girl in every aspect of the word" and was "loved by everyone".
Student Georgina Callander, believed to have been 18, has also been named as among the dead.
She had been studying health and social care at Runshaw College in Leyland, Lancashire.
Armed police have arrested a 23-year-old man in Chorlton, south Manchester, in connection with the attack.
Sitting wearily by a police cordon near Market Street is 19-year-old Joe Barrass. He worked an overnight shift and helped injured people.
He told me taxi drivers were giving free lifts home to people and hotels were helping the injured.
"It's only just started to sink in, I feel numb," he said.
"But it felt like the city came together. It's a tragedy. They were children, teenagers, the fact they had gone after the truly innocent is shocking.
"No-one expected this - let alone at an Ariana Grande concert gig. Stuff like this will never win.
"These people haven't succeeded with what they wanted to do. The love is here for Manchester. They have failed."
A woman, who asked to remain anonymous, agrees. She said she was shocked and disgusted - but determined not to be afraid.
"They are not going to beat us. It's subdued here, but we're defiant. It's quiet but people are walking around. I think whoever has done this is a total coward."
Naomi Hancock, 25, from Radcliffe in Greater Manchester, said it "feels really eerie. It's so quiet, a totally different city".
"It makes me think what kind of world we live in. Manchester is a strong city and I hope we can get through it."
Subrata Sen, a 46-year-old from Bangalore, is visiting Manchester for work and was staying near to the blast site.
He said: "It's really sad. At first we thought something had fallen down, nobody knew what had happened. Manchester is such a welcoming city, it's a warm city.
"People are going about their way of life. We have to carry on, show resilience."
No-one is sitting at the usually crowded fountain at Exchange Square, or walking through the cathedral or past the shops.
People stop and look over the police tape. Some on their own, others in pairs. No noise. Just looking. People pay their respects with flowers, a bunch is left on Corporation Street.
This morning Manchester is not the city I know, love and grew up with. But it's remaining strong.
A peace campaigner whose 12-year-old son was killed by an IRA bomb 24 years ago has offered to help families bereaved in the Manchester bomb attack.
Colin Parry's son Tim was one of two children killed in 1993 when the IRA bombed the nearby town of Warrington.
Mr Parry helped to set up a peace centre in memory of both boys.
He said he will be offering its support services to Manchester families going through "the most unimaginable horror any parent can ever countenance".
At this afternoon's Buckingham Palace garden party the Queen and her guests will observe a minute's silence for the Manchester attack.
Less than 24 hours after the worst terrorist attack in Manchester's history, its people came together to remember the 22 victims who went to enjoy one of the city's favourite pastimes - going to a gig - but never came home.
Basked in early evening sunshine, the mood in Albert Square was sombre but strong. Manchester is a city of glorious, rebellious positivity and thousands were here to make that point in front of the cameras of the world's press.
While some had come to simply pay their respects to those killed and injured by an appalling act, others also wanted to stand firm in the face of horror.
"Love over hate, that's the message," said one woman, finishing off a poster of support, while in another corner of the square, the Manchester Sikh Community handed out free drinks, a gesture to "help the city at a time when things are bad".
As the Town Hall bells chimed six, the throng fell silent - ready, respectful, resilient - so that only the leaves could be heard blowing through the trees.
The silence held for a full five minutes before the Lord Mayor Eddy Newman began to speak.
His was a message of thanks for the emergency services and defiance in the face in the terrorism, words that were met with cheers and loud applause.
He was followed by others with equally unbending speeches.
The Bishop of Manchester, the Rt Rev David Walker, spoke of the city's unerring belief in diversity and unity and said those who would seek to destroy such things were "the very few, but we are the many, we are Manchester".
The victims of the attack, he said, were now "Manchester too", regardless of where they came from.
Greater Manchester Police's Chief Constable Ian Hopkins echoed those words and added the stories of those who came together in the aftermath; of the doctors who came in when they were off shift, the communities who opened their doors to the displaced and the emergency crews who worked tirelessly through the night.
And after the speeches and an impeccably observed minute of silence, an moment of release, as the thousands gathered broke into a chant of the city's name.
But shining out from the midst of it all was poet Tony Walsh's reading of his ode to Manchester, This Is The Place, that captured the moment best.
A run-through of what and why the city is so special, it was met with cheers and a simple ending which summed up the feelings of all those in the square.
"Choose love, Manchester", he said, to an enormous ovation.
Messages of condolence and support have been sent by Manchester's public figures following the terror attack that killed 22 people and injured 59.
Greater Manchester Mayor Andy Burnham said the city would "pull together", adding: "That's what we are. That's what we do. They won't win."
The Bishop of Manchester, the Rt Rev David Walker said we must "commit ourselves to defeat this terrorism".
"Hatred won't win", Salford comedian Jason Manford said on Facebook.
Mr Manford said: "My heart is broken for those poor children and for all those families with an empty house tonight. Just can't believe it. Can't stop crying."
Inviting people to a vigil which was held at Albert Square on Tuesday evening, Mr Burnham tweeted: "We are grieving today but we are strong".
Books of condolence are open at Manchester Town Hall and on the council's website.
Rt Rev David Walker said people must not allow terrorists "to dictate the way we live".
"Manchester's a wonderfully diverse city, that's one of the things I really love about it and we can pull together.
"We've pulled together in the past, we had a terrorist bomb 21 years ago so we're not unused to these events.
"But it is a time for all of us to pray for the wounded, for the dead, for their families, but to commit ourselves to defeat this terrorism as we've defeated terrorism in the past," he said.
Coronation Street stars also paid tribute with Brooke Vincent, who plays Sophie Webster in the soap, tweeting it was "absolutely heartbreaking".
Tina O'Brien, who plays Sarah Platt, tweeted: "I love my home city, stay strong Manchester".
Labour Manchester Central candidate Lucy Powell praised the solidarity and support of the city's people.
"The people have come together to try and support families, children that have been separated from their parents, and that is the spirit of our city and that spirit will never be killed, will never die", she said.
Manchester United's players held a minute's silence in memory of the victims and footballers connected with the city have been using social media to express their sadness and support.
The club tweeted condolences from boss Jose Mourinho, who said: "I know, even during my short time here, that the people of Manchester will pull together as one."
Former Manchester United and England captain, Bryan Robson, tweeted that it was "such sad news".
Phil Neville posted a picture of the city on Twitter, with the words "we will not be defeated, we will stand strong" and said: "saying my prayers for the families affected and for my city - utter despicable act".
Using the hashtag #StandTogether, Rio Ferdinand tweeted that his "thoughts & prayers are with all the families & friends affected" by the attack.
Simple Minds confirmed their show at Bridgewater Hall in Manchester will go ahead later, saying their "thoughts and prayers" were with those affected.
But Take That have postponed their show in Liverpool "out of respect to all of the people and their families that were affected by the horrific incident".
Three more men have been arrested as police continue to investigate whether Manchester Arena bomber Salman Abedi acted alone.
Police arrested the three in the city on Wednesday. Abedi's 23-year-old brother was arrested on Tuesday.
Abedi killed 22 and injured 64 when he blew himself up outside an Ariana Grande concert on Monday night.
The UK terror threat level is now up to its highest level of "critical", meaning more attacks may be imminent.
It means military personnel are being deployed to protect key sites.
The Palace of Westminster has been closed to the public following police advice, and will not re-open until further notice, a statement on its website said.
And the Changing the Guard ceremony at Buckingham Palace has been cancelled on Wednesday to allow for the redeployment of police officers, the Ministry of Defence said.
Home Secretary Amber Rudd said: "[Monday's attack] was more sophisticated than some of the attacks we've seen before, and it seems likely - possible - that he wasn't doing this on his own."
BBC security correspondent Frank Gardner said that the bomber is thought to have been a "mule", using a device built by someone else.
Police investigating the Manchester Arena bomb attack have stopped sharing information with the US after leaks to the media.
UK officials were outraged when photos appearing to show debris from the attack appeared in the New York Times.
It came after the name of bomber Salman Abedi was leaked to US media just hours after the attack, which left 22 dead.
Theresa May said she would tell Donald Trump at a Nato meeting that shared intelligence "must remain secure".
The US's acting ambassador to the UK "unequivocally condemned" the leaks in a BBC radio interview.
"These leaks were reprehensible, deeply distressing," Lewis Lukens said.
"We have had communications at the highest level of our government ... we are determined to identify these leaks and to stop them.
Meanwhile, the Queen has been to the Royal Manchester Children's Hospital visiting some of the injured as well as members of the emergency services.
While there she paid tribute to Manchester and the "extraordinary" way the city had responded to Monday's attack at an Ariana Grande concert, in which 116 people were also injured.
In total eight men are now in custody following the bombing carried out by Manchester-born Abedi, a 22-year-old from a family of Libyan origin.
The arrests have been "significant" while searches of premises have also yielded items "important to the investigation", Greater Manchester Police said.
It has also emerged two people who had known Abedi at college made separate calls to a hotline to warn the police about his extremist views.
A Whitehall source said Abedi was one of a "pool" of former subjects of interest whose risk remained "subject to review" by the security service and its partners.
In other developments:
◾A minute's silence was held at 11:00 BST in remembrance of those who lost their lives or were affected by the attack
◾Two men were arrested following a search of an address in the Withington area of Greater Manchester on Thursday morning, taking the number of people held to eight
◾ Manchester City and Manchester United have jointly pledged £1m to an emergency fund set up to support the victims
◾ A possible suspicious package was declared safe after army bomb disposal experts were called to a street in Hulme, near Manchester city centre
◾The Conservatives and Labour are to resume general election campaigning on Friday
Greater Manchester Police hope to resume normal intelligence relationships - a two-way flow of information - soon but is currently "furious", the BBC understands.
Its chief constable Ian Hopkins said the recent leak had caused "much distress for families that are already suffering terribly with their loss.".
The force - which is leading the investigation on the ground - gives its information to National Counter-Terrorism, which then shares it across government and - because of the Five Eyes intelligence sharing agreement - with the US, Australia, Canada and New Zealand.
Three men from London have been charged with offences under the Terrorism Act over an alleged UK terror plot.
Umar Ahmed Haque, 24, and Muhammad Abid, 27, both from Newham in east London, were arrested on 17 May along with Abuthaher Mamun, 18, from Barking.
They have been remanded in custody and will appear before Westminster magistrates on Friday.
A fourth man, Nadeem Ilyas Patel, 25, from Newham, faces a charge of conspiring to possess a firearm.
Mr Haque has been charged with preparing to commit acts of terrorism and four counts of possessing records useful for committing or preparing acts of terrorism.
Mr Abid has been charged under terror laws with failing to disclose information and Mr Mamun is accused of assisting another to commit acts of terrorism.