Here's what we know so far.
Armed police and ambulances were called to reports of a white van hitting several people on London Bridge  22:08 BST on Saturday.
The area and nearby railway stations were closed. Eyewitness reports said the van mounted the pavement of the bridge.
BBC reporter Holly Jones, who was on the bridge at the time, said: "A white van driver came speeding - probably about 50mph - veered off the road into the crowds of people who were walking along the pavement.
"He swerved right round me and then hit about five or six people."
Police have said there has been "more than one" person killed on London Bridge.
British Transport Police confirmed at 23:15 that there were "a number" of casualties and said there was an "incident that possibly involved a van and a knife".
London Ambulance Service said "multiple resources" were sent to the scene.
The Metropolitan Police confirmed a second armed response to nearby Borough Market where there were reports of stabbings. Police said shots have been fired.
A third police unit was sent to the Vauxhall area.
Injured people are being treated on London Bridge and being moved from the scene.
Armed police are also at Borough Market, which is on the south side of London Bridge. The Met confirmed shots were fired.
The area around the bridge has been cordoned off.
London Bridge and Borough stations have been closed and trains are passing straight through.
Network Rail also said Waterloo East, Charing Cross and Cannon Street stations have been closed.
Police boats are searching the River Thames for anyone who may have fallen from the bridge.
Armed police are also understood to be in the Vauxhall area of south London.
Prime Minister Theresa May and Mayor of London Sadiq Khan are being kept "regularly updated" on events.
The prime minister will chair a meeting of the government's Cobra emergency committee on Sunday.
Armed police are responding to security incidents in central London, at London Bridge and nearby Borough Market, amid reports a van has been driven at pedestrians as well as a number of stabbings.