The murder of Arab-Israeli exchange student Aiia Maasarwe in Melbourne's north has sent shockwaves through the city and led to an outpouring of grief and anger.

Here's what we know so far about what happened.

An adventure abroad

21-year-old Ms Maasarwe came to Melbourne about five months ago for a one-year exchange program at La Trobe University, as part of her business studies at Shanghai University.

Aiia Maasarwe has been remembered as "cheerful" and kind by friends. ( Instagram: @aia0206 )

Described as intelligent, funny and gifted in learning new languages, Ms Maasarwe planned to use her degree to work alongside her father at his business in China.

Her Instagram account shows she had immersed herself in her new home, with a visit to the Shrine of Remembrance and the Grampians National Park among her most recent travels.

Her account is headlined with the words "the best is yet to come".

Ms Maasarwe's family said she had loved her first few months of adventures.

They have been devastated by her violent death in a city they thought was safe, and her father has flown to Melbourne.

The Israeli embassy is supporting the family to eventually take her body back to Israel for burial.

Aiia Maasarwe told family she was enjoying exploring Melbourne. ( Instagram: @aia0206 )

A park meet-up and a comedy show

On Tuesday night, she had attended an event at Flagstaff Gardens for people keen to practise their English between about 7:00pm and 8:00pm.

Event organiser Arun Chandran said Ms Maasarwe had joined a few of the group's tours in the past, including one to see kangaroos in the wild in December last year.

"She was very friendly, knowledgeable, easy-going, and someone who knew a lot. It was quite refreshing to talk to her," he said.

"She wanted to I think speak Spanish as a next language, so she was always someone who wanted to challenge herself and learn something new."

Mr Chandran said he only realised Ms Maasarwe had been killed when he saw CCTV footage released by police.

Aiia Maasarwe was learning Chinese alongside her business studies. ( Instagram: Ruba Photography )

"It's just a sense of disbelief," he said. "She was just here on a student visa, trying to better her career, and they should feel safe in a city like Melbourne."

After that event, she attended a comedy show at The Comics Lounge in North Melbourne.

Grainy CCTV footage from North Melbourne shows she left the club wearing a white or grey t-shirt with writing on it, and a dark skirt.

The last footage of Aiia Maasarwe shows her leaving The Comics Lounge. ( Supplied: Victoria Police )

A phone call between sisters

After the show, friends drove Ms Maasarwe to a Bourke Street tram stop in Melbourne's CBD, where she caught a Route 86 tram about 10:50pm.

That tram wound its way to Bundoora in the city's north, where Ms Maasarwe had been living while she studied at the La Trobe University campus nearby.

About 12:10am, she got off at a stop at the intersection of Plenty Road and Main Drive.

She was a little more than a kilometre from home.

Police have increased patrols in the area while they hunt Aiia Maasarwe's killer. ( ABC News )

Police say she had left the tram and was speaking on the phone to her sister, who is overseas.

Detectives believe it was then that she was attacked on the footpath, less than 50 metres from the tram stop.

"Sadly, her sister was talking to her on the phone," Detective Inspector Andrew Stamper said.

"The phone then appeared to fall to the ground and she couldn't contact her. We think that's the time.

"She heard the sound of the phone falling to the ground and heard some voices and that was it."

Sorry, this video has expired Police appeal for public help to find Aiia Maasarwe's killer

A devastating discovery

Detective Inspector Stamper said he would not detail Ms Maasarwe's injuries out of respect for her family.

"All I will say is, this was a horrific attack. This was an absolutely horrendous, horrific attack inflicted on a completely innocent young woman who was a visitor to our city," he said.

About 7:00am on Wednesday, the body of Ms Maasarwe was discovered by passers-by outside the nearby Polaris shopping centre.

The death has prompted police to ramp up their presence in the area where the attack occurred in response to community fears about the killer still at large.

La Trobe University has also vowed to increase security around its nearby campus.