Police say a lone male attacker carrying an improvised explosive device was responsible for the bombing at Manchester Arena.
The explosion at the end of a sold-out Ariana Grande concert has killed 22 people and injured 59 others.
Greater Manchester Police chief constable Ian Hopkins has confirmed that children are among those who died.
Investigators are trying to establish whether the attacker, who also died at the scene, was part of a wider network.
A detailed forensic search is under way at the arena, and nearby Manchester Victoria train station remains closed.
Several young people have been reported missing following the explosion – with concerned friends and relatives appealing for information on Twitter. A hotline has been set up for those with concerns over loved ones who remain unaccounted for.
Footage from inside the venue showed fans running and screaming after the explosion, which happened at about 10.35pm last night.
Ariana Grande, who was not harmed in the attack, tweeted: “broken. from the bottom of my heart, i am so so sorry. i don’t have words.” Her manager Scooter Braun said they mourned “the lives of children and loved ones taken by this cowardly act”.
Manchester Arena said the incident had happened outside the venue “in a public space”.
Others said it happened close to the ticket offices in a foyer area. Concert-goers affected by the suspected terror attack were offered shelter by residents, taxi drivers offered free rides and a hotel near the venue took in dozens of children.
Manchester Mayor Andy Burnham tweeted: “My heart goes out to families who have lost loved ones, my admiration to our brave emergency services. A terrible night for our great city.”
Theresa May said her thoughts were with the victims and families of those affected and has condemned “what is being treated by the police as an appalling terrorist attack”.
Election campaigning by the Conservatives, Labour and UKIP has been suspended, with other parties expected to do the same. Home Secretary Amber Rudd also condemned the “barbaric attack, deliberately targeting some of the most vulnerable in our society”.
She said: “The full details of exactly what happened are still emerging, but I am proud of the police and first responders who reacted to this tragic incident so swiftly.”
An emergency COBRA meeting is expected to take place in Downing Street at 9am.
Labour leader Jeremy Corbyn said: “I am horrified by the horrendous events in Manchester last night. “My thoughts are with families and friends of those who have died and been injured. Today the whole country will grieve for the people who have lost their lives.”
Manchester Fire and Rescue tweeted a statement to say crews were helping police and paramedics at “the scene of this horrific incident”. “Our thoughts and prayers go out to everyone affected and especially the families who lost their loved ones tonight – utterly heartbreaking,” they said.
North West Ambulance Service Trust has urged people to only call in the case of life-threatening emergencies.
“If you require our assistance over the next few hours, please bear with us we have a large number of resources at the incident in Manchester,” the trust tweeted.
Two US officials speaking to the Reuters news agency suggested that initial signs pointed to a suicide bombing. If it is confirmed to be a terrorist attack, the explosion will become the worst atrocity in the UK since the deaths of the 52 victims of the 7/7 London bombings in 2005. In the capita;, the Met police urged people to stay “vigilant” and added: “You’ll see more police in London today.”
:: People concerned about loved ones can call 0161 856 9400 or 0161 856 9900. To report any concerns about terrorism, call the anti-terrorist hotline on 0800 789 321.