Officers found a body in a river in west London on Tuesday night.
The 14-year-old schoolgirl was last seen on CCTV walking along the towpath next to a canal near her home.
Newsbeat reporter Tamsyn Kent lives in Hanwell, in Ealing, west London, and she explains what it's like to live there now.
"I live just around the corner from Alice's family. I don't know them. Until a few weeks ago, I'd never heard of her.
"But a few days after she went missing, I tied a yellow ribbon to a lamp post outside my house.
"Like everyone else in Hanwell I was showing support for the Find Alice campaign.
"Now the whole town's covered with yellow ribbons.
"On the high street at the end of the road, you can see them in the trees, on the railings, the bins, on people's cars.
"Her photo is up in every shop window and on the bus stops.
"Now through the Facebook page her friends and family have set up they're asking people to take them down.
"Last Sunday, 6,000 people and I ran through this bit of Hanwell in the Ealing half-marathon.
"It was amazing to see most of the runners wearing the Find Alice yellow ribbon.
"It's had a huge impact on the town. It's everywhere you go and all people do is talk about the investigation and when she'll be found.
"But this morning, everyone I've spoken to is devastated that there's a body.
"It's what no-one wanted to hear, but as the weeks went by it seemed sadly inevitable.
"On the local Facebook group, Hanwell Friends, someone posted, 'I think Hanwell's collective heart just broke.'"
"About a 10-minutes walk away is the local park.
"The River Brent, where the body's been found, runs right through it. It's not deep.
"The kids paddle here in the summer. And two miles from here is where the police's main suspect, a Latvian, Arnis Zalkalns, lived before he disappeared.
"Walking back past the golf course, which has become the makeshift police headquarters, I think everyone feels so deeply for Alice and her family.
"And also devastated that this should happen to our town."
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Police investigating the disappearance of teenager Alice Gross have started a murder investigation.