Police have said they know of one armed assailant, but there could be more.
Paramilitary officers cordoned off several blocks around the cafe as negotiators tried to defuse one of the biggest security scares in Australia for decades. Snipers and a SWAT team took up positions around the cafe and police helicopters flew overhead.
A photo of hostages with their hands up was posted on Twitter by Australia's 7 News, as well as a photo of a black flag with Arabic writing being hung up at the window of the cafe.
Later, a man who works in the Lindt Chocolate Cafe, and arrived for work just after the siege started, said he saw one of his colleagues pressed up against the window.
Nathan Grivas told The Guardian it was already locked when he arrived.
"I didn't get a good look at them, as soon as I saw the gun all I wanted to do was get out," he said.
A man who identified himself as Bruno, a worker at the cafe, told the Australian Broadcasting Corp: "I walked up to the door and then everyone was sitting down and the door's locked which is pretty weird because it's never locked and there was one guy walking around with a hat and a beard."
Martin Place is a plaza in the heart of the city's financial and shopping district which is packed with holiday shoppers at this time of year.
Who are the kidnappers - and what do they want?
The precise demands of the hostage-taker or hostage-takers are not yet known. But the black and white flag displayed in the shop shows the Shahada - a testament to the faith of Muslims which is declaring belief in the oneness of God and the acceptance of Mohammad as God's prophet.
It can be a benign symbol and appears across the Islamic world, including on the Saudi Arabian flag. But it has also been popular among Sunni Islamist militant groups such as Islamic State and al Qaeda.
An image has been circulating online of the alleged hostage-taker wearing what looks like a bandanna with Arabic writing.
Ray Hadley, a radio disc jockey, said he had been contacted by a hostage and could hear the suspected gunman issuing orders in the background. Police declined to comment.
Network 10 reported that two female hostages had called with claims from the gunman that two bombs were planted elsewhere in the city. Social media posts by alleged hostages claimed the gunman wanted to speak directly with Prime Minister Abbott.
Channel Ten said it had spoken to two of the hostages inside the cafe and the man holding them had made a series of demands, including for the delivery of an Islamic State flag.
"Our TenNews team have spoken directly to 2 hostages inside the cafe... They are confirming 2 demands from the perpetrator," the network tweeted.
"He needs the ISIL flag to be directly delivered to the cafe; And his 2nd request is to speak to the Prime Minster.
"They also state there are 4 bombs... two inside the Lindt cafe at Martin Place - and two further in the Sydney CBD."
Police said they were aware of media reports but said the "situation is contained in one area".
Concerns about an attack in Australia by Islamists have been growing for more than a year, with the security agency raising its national terrorism public alert to "high" in September.
That month, a spokesman for the Islamic State urged supporters in Western nations, including Australia, to attack civilians or military personnel at home.
How many people have escaped - and who is still inside?
Many of those inside the cafe would have been taken hostage as they stopped in for their morning coffees. The exact number of hostages is still unknown.
Glenn Connley, a Channel 7 journalist, told BBC News he believes there are two or three staff members inside the cafe as well as up to 10 or 11 customers. But other reports suggested as many as 50 people were inside.
So far, five people are known to have escaped. Six hours after the hostage crisis began, three men were seen running from a fire exit of the Lindt Chocolat Cafe in downtown Sydney.
Shortly afterward, two women sprinted from the cafe and into the arms of heavily armed police. Both were wearing aprons with the Lindt chocolate logo, indicating they were cafe employees.
"We do not have any information that suggests that anybody is harmed at this stage," New South Wales Police Deputy Commissioner Catherine Burn said, after the first three hostages had emerged.
One of the hostages managed to call her fiance and tell him she loved him before hanging up earlier today, according to the Guardian.
The man, who has not been named, said she must have managed to call him from another room and she said she loved him and couldn't wait to see him before hanging up.
He said she sounded scared but he thought it was brave. He then texted her and an hour later got a reply again saying she loved him.
What has been the reaction?
Australian Prime Minister Tony Abbott said there were indications the incident could be "politically motivated".
He said: "Our thoughts and prayers must above all go out to the individuals who are caught up in this.
"I can think of almost nothing more distressing or terrifying than to be caught up in such a situation, and our hearts go out to those people."
He said there are "some indications" that the incident could be politically motivated, but said the exact motive is yet to be established.
Mr Abbott said: "We don't yet know the motivation of the perpetrator. We don't know whether this is politically motivated, although obviously there are some indications that it could be.
We have to appreciate that, even in a society such as ours, there are people who would wish to do us harm.
On the Lindt Chocolate Cafe Australia's Facebook page, a post appeared around five hours into the ongoing incident which said: "We would like to thank everyone for their thoughts and kind support over the current situation at the Lindt Chocolate Cafe at Martin Place.
"We are deeply concerned over this serious incident and our thoughts and prayers are with the staff and customers involved and all their friends and families.
"The matter is being dealt with by the authorities and we are waiting for any updates from them."
Prime Minister David Cameron said he had been briefed overnight on the siege, adding: "It's deeply concerning and my thoughts are with all those caught up in it."
