What We Know

• The police on Thursday revised the death toll to four from five. The victims were Kurt W. Cochran, an American tourist in his 50s; Aysha Frade, 43, a British teacher; and Police Constable Keith Palmer. . About 40 others were wounded.

• The London police identified the assailant, who died in the attack, as Khalid Masood, 52, who had an extensive criminal history but no terrorism convictions. Mr. Masood was born in Kent, in southeastern England, and recently lived around Birmingham, the city where the car used in the attack had been rented.

• Eight people were arrested in London and Birmingham after searches at six properties around Britain. The police said that “a full counterterrorism investigation was underway.”

• The Islamic State claimed responsibility for the attack, describing the assailant as a “soldier.”

• The casualties included 12 Britons, at least four South Koreans, three French children, two Romanians, two Greeks and citizens of several other countries.

• Parliament Square and its immediate vicinity remained cordoned off to the public Thursday morning, but lawmakers have resumed their normal business.

What We Don’t Know

• Whether the authorities shared information about Mr. Masood. The London police said that “Masood was not the subject of any current investigations, and there was no prior intelligence about his intent to mount a terrorist attack.” But Prime Minister Theresa May said earlier that MI5, the domestic counterintelligence agency, had looked into the assailant “in relation to concerns about violent extremism.”

• The severity of the injuries among the 40 or so wounded.

• The veracity of the Islamic State’s claim, and the extent to which the group was involved in planning and carrying out the attack.