The Westminster attacker - 52-year-old Khalid Masood - had a range of previous convictions but none terrorism-related.
Islamic State has claimed Masood - whose birth name was Adrian Elms - was one of its "soldiers".
He "carried out the operation in answer to calls to target the people of coalition states", the terror group said.
According to a Sky source who met him in a professional capacity, he had a wife and three children.
The source described Masood as "a big bloke", adding: "He looked like he was a bodybuilder, (you) wouldn't want to mess with him."
He added that Masood was a "very religious, well-spoken man", who had "converted" to Islam.
"You couldn't go to his home in Birmingham on Friday because he would be at prayer," the source said.
According to reports Masood had previously worked as an English teacher, though not in any of England's state schools.
Some reports suggested he had spent four years in Saudi Arabia, leading to speculation he may have been radicalised there.
Police said Masood had been "known by a number of aliases".
While he was born in Kent on Christmas Day 1964, detectives believe he had been living most recently in the West Midlands.
His name is also registered as living at addresses in Brighton, Eastbourne, Luton and London.
A neighbour at his most recent address in Winson Green, Birmingham, said Masood was a keen gardener who had a wife and young child.
The neighbour said her experience of him was of a "nice man".
In a statement, the Metropolitan Police said there was "no prior intelligence about his intent to mount a terrorist attack".
Masood "was not the subject of any current investigations", they said.
Nevertheless, "he was known to police and has a range of previous convictions for assaults"
These included convictions for GBH, possession of offensive weapons and public order offences, spanning 20 years from 1983.
According to a court report in 2000, he was jailed for two years for slashing a man's face with a knife.
Three years later, after leaving jail, Masood was accused of stabbing a man in the nose, leaving him needing cosmetic surgery.
He was jailed for another six months.
He has not been convicted for any terrorism offences, police confirmed.
Some of those Masood was involved with included people keen to travel to join jihadi groups overseas, a US government source said.
However, Masood "himself never did so", the source added.
The Sun said Masood stayed in the Preston Park Hotel on the outskirts of Brighton on the night before the attack.
Hours before carrying out the murders, he reportedly told hotel staff as he checked out that he was he was going
He added: "It isn't what it used to be."
Earlier, Theresa May said Masood was a "peripheral" figure who had once been investigated by MI5 over concerns about violent extremism.
Home Secretary Amber Rudd defended the security and intelligence agencies to Sky News, even though "one did get through".
She said: "The fact that he was known to them doesn't mean that somebody has 24-hour cover.
Police have revealed that five men and three women have been arrested on suspicion of preparing terrorist acts.
The suspects were held in raids in London and Birmingham.
Anyone with any information about Masood can call the Anti-Terrorist Hotline 0800 789 321.
:: Sky News will be showing a special programme - Terror In Westminster - at 7.30pm tonight