The attack on the upmarket Westgate Shopping Centre in Nairobi unfolded at around noon local time (09:00GMT), as the building was packed with shoppers and people having lunch.
The multi-storey mall - owned by an Israeli businessman - has restaurants, cafes, banks, a large supermarket and a cinema.
The centre has six levels - a basement, three levels devoted to shopping, eating and leisure, and two more containing offices and a dental practice.
When the attack began, a disputed number of gunmen were thought to have entered the building from three points.
According to witnesses sitting outside ArtCaffe on the ground floor, one group armed with assault weapons drove up to the main entrance. The attackers began firing and throwing grenades, causing panic as shoppers fled the gunfire.
Simultaneously, witnesses said a second group made its way onto the second floor of the building via a rooftop car park.
A children's cooking competition was taking place in the car park and a number of children and adults are believed to have been killed here - including the popular radio DJ Ruhila Adatia-Sood.
A third group of attackers is believed to have entered the building down a ramp into a basement area.
Senior security sources have told the BBC that in the weeks leading up the siege, Islamists had hired a shop in the mall. This gave them access to service lifts, enabling them to stockpile weapons and ammunition.
The BBC understands the attackers set up a base using a ventilation shaft on the first floor.
According to some reports, the attackers made attempts to separate Muslims and non-Muslims, with Muslims allowed to leave the mall unharmed.
A number of people are believed to have been taken hostage and held in a cinema and a casino on the second floor, while others were held hostage in the basement.
When police and security forces arrived on the scene, their efforts initially focused on rescuing those people trapped inside the building, as gunfire and explosions continued to echo around the mall.
Some reports claim the first police officers did not arrive until about 12:30.
At around 15:00, Kenya Defence Forces (KDF) troops were deployed, entering the mall to confront the militants.
Gun battles raged throughout Saturday afternoon, with one group of attackers apparently barricading themselves in the two-level Nakumatt supermarket.
Having pre-positioned weapons in the preceding days, the attackers were able to re-arm quickly and repel Kenyan security forces
Late on Saturday, there was a change of tack by the militants, according to security sources. They rolled out heavy-calibre machine guns, exploiting the moment control of the rescue efforts switched from the police to the military.
Some security sources have suggested there was a breakdown in control when the military took over and soldiers launched an "uncontrolled shooting spree".
By the end of Saturday, the death toll stood at 39 with more than more than 1,000 people evacuated.
The security operation continued into the night with sporadic gunfire and explosions.
Gunfire and explosions continued to echo around the mall on Sunday morning.
By midday - 24 hours after the attack began - the death toll stood at 59, with about 1,000 people rescued.
Interior Minister Jospeh Ole Lenku said that between 10 and 15 attackers remained barricaded inside the mall, but that security forces had control of the CCTV room.
There are reports via the Israeli military intelligence analysis website Debkafile that Israeli security men were assisting the Kenyan military in the operation against the attackers.
At 18:45, two helicopters were seen landing on the roof in an apparent effort to retake the mall. Shortly afterwards a large explosion was heard from inside.Monday 23 September
On Monday morning, a series of loud explosions and heavy gunfire was heard and thick black smoke began billowing from the complex as security forces launched another assault.
Interior Minister Lenku told journalists that almost all the hostages had by then been evacuated - indicating that some remained unaccounted for - two of the militants had been killed and several had been injured.
He said 62 people had died but the security forces were in control of every floor of the shopping centre.
As night fell, a fire was seen burning at the shopping centre and security forces continued the operation to clear the building of militants.Operation ends
Early on the Tuesday after the attack, a senior police source declared the operation to clear the building was "over", however journalists outside reported that sporadic gunfire was continuing.
The fire in the mall - which Kenyan officials said was started by the attackers burning mattresses - caused part of the roof to collapse.
Video footage showed that part of the car park on the second floor roof had completely collapsed, with a pile of rubble and smouldering vehicles visible below.
There have been allegations of mass looting by uniformed officers after the attack, as shop owners returning to the mall reported missing money, camera equipment and other goods.Aftermath
A total of 61 civilians and six security officers have been confirmed dead as a result of the attacks. The Kenya Red Cross lists 23 people as still missing. It is thought that the death toll could rise, with bodies possibly concealed under the rubble.
Two charred bodies pulled from shopping centre on Thursday 17 October were "highly likely" to be two of the attackers, a Kenyan MP told the BBC.
However, in the weeks since the attack, there have been conflicting reports about the number of gunmen involved. Initially it was estimated to be between 10 and 15 - but later it was suggested to be as low as four to six.
Interior Minister Joseph Ole Lenku has said he "could not rule out the possibility that when we were evacuating people in the first stages of the operation, it is possible some (of the attackers) could have slipped out".
The Kenyan authorities have released the names, or nicknames, of four suspects, but have given few other details.
They were identified as Abu Baara al-Sudani, Omar Nabhan, Khattab al-Kene and Umayr. The Kenyan military said they all died in the security operation.
The Somali militant group al-Shabab said its members staged the attack in response to Kenya's army carrying out operations on Somali territory.
There are about 4,000 Kenyan troops in the south of Somalia, where they have been fighting the militants since 2011.
The BBC's Newsnight programme has revealed that one of the suspected attackers was a 23-year-old Somalia-born Norwegian national, Hassan Abdi Dhuhulow.
His family fled to Norway in the 1990s, but he returned to Somalia in 2009 and allegedly joined the Somali militant group.
Al-Shabab has said via Twitter that 137 hostages died after government troops used chemical agents to end the siege, but its statement cannot be verified and the government has denied its claims.
There have been unconfirmed reports that Americans and a British woman were among the attackers - but these have not been substantiated.