Here is what we know so far:
** Among the dead are Police Officer Keith Palmer and the assailant.
** 29 people remain in hospital receiving treatment.
** Mrs May said the attacker was a British citizen who was known to Police and Security Services.
** Eight people have been arrested and raids have taken place in London, Birmingham and elsewhere.
** The attacker, armed with two large knives, mowed down pedestrians with his car on Westminster Bridge on Wednesday afternoon.
** The knifeman was shot dead moments later by another Officer.