Here is what we know so far:
A small van spend into a crowd of customers and staff at outdoor tables belonging to a restaurant in the historic centre of Münster in north-west Germany at 3.27pm on Saturday, killing two.
German media reported that those killed were waiters at the “Grosser Kiepenkerl” restaurant not far from the city's cathedral.
Some 20 people were wounded, around ten of them “seriously”, interior minister of North Rhine-Westphalia state Herbert Reul said.
The driver stopped the van immediately after the impact, shooting himself inside the vehicle according to police.
Who was the driver?
The driver was “a German, and not, as has been claimed everywhere, a refugee or something like that,” Reul said.
Matching reports from several German media outlets said the attacker was a man aged around 48 with psychological problems. Television news reported that he had recently attempted suicide and made known that he planned a more spectacular attempt.
Several reports pointed to a past of petty crime and drug dealing.
The man was employed as an industrial product designer and struggled with problems at work.
Broadcaster ZDF said he had known connections with far-right organisations, while new website Spiegel Online reported an assault rifle was found at his Muenster apartment close to the scene of the crime.
Investigators found a “suspicious object” in the van, which Die Welt newspaper reported was a pistol connected to a wire leading underneath the van's floor carpeting.
Suspecting a booby trap, the police called in bomb disposal experts.
What motivated the attacker?
There is so far no clear indication of the attacker's motive, but authorities said they had ruled out an Islamist background to the act.
Germany has been on especially high alert for such terrorist attacks since a Tunisian asylum seeker rammed a truck into crowds at a Berlin Christmas market in December 2016.
“There is no indication at the moment that there is any Islamist connection,” state interior minister Reul said.
Police will attempt to determine whether the driver wanted to commit a “murder-suicide”, taking other people with him in the process of killing himself.
Did the perpetrator act alone?
Police initially said witnesses had spotted potential accomplices exiting the van immediately after the attack. But there is so far no evidence to back up this theory.
Police locked down a wide area around the scene of the attack immediately afterwards, but gradually opened some roads up to traffic again as evening drew in.