He may have been an ISIS supporter
While U.S. authorities investigate whether Sunday's shooting has any link to international terrorism, ISIS claimed responsibility for the attack
In a radio broadcast, ISIS referred to Simpson and Soofi as two of its "soldiers" and and threatened more attacks. But it's unclear whether the terror group in Iraq and Syria actually had contact with Simpson or Soofi, who both lived in Phoenix.
Moments before the shootout, Simpson posted an ominous tweet with the hashtag #texasattack: "May Allah accept us as mujahideen."
The tweet also said Simpson and his fellow attacker had pledged allegiance to "Amirul Mu'mineen," which means "the leader of the faithful." CNN terrorism analyst Paul Cruickshank said that probably refers to ISIS leader Abu Bakr al Baghdadi.
Earlier, Simpson had asked his readers on Twitter to follow an ISIS propagandist.
After the shooting, the same propagandist tweeted: "Allahu Akbar!!!! 2 of our brothers just opened fire."
Both Twitter accounts have been deactivated.
He has a rap sheet
In 2011, Simpson was convicted of making a false statement involving international and domestic terrorism.
Prosecutors said he told FBI agents that he had not discussed traveling to Somalia
to engage in "violent jihad" -- when, in fact, he had, according to an indictment.
Simpson was sentenced to three years of probation, court records show.
His former lawyer, Kristina Sitton, told CNN that Simpson ended up on the federal no-fly list. In fact, he contacted her once after trying to get on a plane at a Phoenix airport, only to be turned away.
He was a 'very devout Muslim'
That's according to Sitton, who spent many hours over about two years in her office with Simpson while representing him in the Somalia case.
When the meetings ran long, the attorney recalled Simpson asking to leave to pray somewhere quiet.
"He was a very devout Muslim," said Sitton, who sensed Simpson was trying to convert her and her staffers but never saw him as a threat. "... I can tell you with absolute certainty that I didn't observe anything that had anything to do with radicalization."
In fact, Sitton said, "there were no signs" that Simpson would pull off an attack like the one in Garland.
"He was a very kind-hearted, respectful young man," the lawyer added. "He always treated me with respect."
He had 'a good demeanor'
That view was seconded by the president of the Islamic Community Center of Phoenix, where both Simpson and Soofi worshiped.
Usama Shami said Simpson came regularly until around 2010 or 2011, about the time the FBI arrested him on the false statement charges. Soofi came less frequently.
Simpson "was a gentle person," Shami said. "He always had a good attitude, a good demeanor."
Like others at the mosque, Shami said he was stunned to hear about the attack Sunday night.
"They didn't show any signs of radicalization or any signs of even thinking about those things in that manner," he said. "So when that happens, it just shocks you. 'How good did you know these people?' That's the question that people ask themselves."
His family is stunned, too
On top of their grief, Simpson's relatives are struggling to come to terms with his involvement in the attack.
"We send our prayers to everyone affected by this act of senseless violence, especially the security guard who was injured in the line of duty," Simpson's family said in a statement.
"We are sure many people in this country are curious to know if we had any idea of Elton's plans. To that we say, without question, we did not. Just like everyone in our beautiful country, we are struggling to understand how this could happen. ... We are heartbroken and in a state of deep shock as we grieve."
He and Soofi were roommates
Their neighbors in Phoenix said they had no clue about what Simpson and Soofi were plotting to do.
Ariel Whitlock was actually about to buy a car from Simpson. She was horrified to see the same black Chevrolet Cobalt, damaged from the attack, on the news.
"I'm getting goose bumps thinking about it right now just because I wanted to buy that car," she told CNN's Kyung Lah. "On the news, I see it, it's just blown up. I'm like, 'I was going to purchase that car.' "
Whitlock said she's sickened by the possibility that, had she bought the car, the money could have gone to fund an attack.
"Maybe he's just gonna go plot something and you're giving the money to help him go plot something," she said. "It's just crazy."
He died near where he was born
Soofi was born in Garland and spent the first three years of his life there, his mother said, according to The Dallas Morning News
"He was raised in a normal American fashion," Sharon Soofi said. "Yes, he was very politically involved with the Middle East. Just aware of what's going on. I don't know if something snapped or if Elton Simpson was just working on him."
He left behind an 8-year-old son
Sharon Soofi also said her son had an 8-year-old boy whom he adored.
"He put his son above everything," she said
. "The hard thing to comprehend is why he would do this and leave an 8-year-old son behind."
He went to a prestigious private school
Soofi's father is Pakistani, and his mother is American, a source with knowledge of the family told CNN.
After his parents divorced, Soofi and his brother moved to the United States in 1998 to live with their mother and gradually lost touch with many of their friends in Pakistan
, the source said.
In the 1990s, Soofi attended a prestigious private school in Islamabad.
He wasn't on the FBI's radar
Unlike Simpson, who had been convicted of a terror-related charge, Soofi was relatively unknown to federal investigators, a law enforcement official told CNN.
Authorities knew of no indication the two planned to launch Sunday's attack, another law enforcement official said.
He had asked for forgiveness
Soofi's Facebook page reveals strong opinions, but no call to violence.
But a note from four years ago shows he asked Allah for forgiveness for every sin -- both intentional and unintentional.
He was a helpful neighbor
Tim Rains remembers Soofi helping him when he had a heart condition about a year ago.
As Rains was coming home, he collapsed on a stairwell. Soofi noticed.
"He seen all that, and he came over and offered me help," Rains said.
So how does he reconcile the notion that his neighbor also tried to shoot people in Texas?
"Oh, it's easy, everybody has a good side to them," Rains said. "If you see somebody hurting like that, you're going to help them. I think he went to Texas to shoot people for a reason."