The escalation follows the breakdown of a week-long ceasefire brokered by Russia and the United States earlier in September that had brought brief respite to the battleground city.
More than 170 people have been killed since the latest Russian-backed offensive started, according to the Syrian Observatory for Human Rights.
Residential buildings have been reduced to rubble and residents of rebel-held east Aleppo face severe shortages of food, medicines and water. Here's a brief overview of the situation:
- The offensive starts -
On September 22, 2016, the Syrian army announces a major offensive aimed at retaking rebel zones in east Aleppo.
The military warns residents to keep away from posts held by "terrorists" in eastern districts, which rebels have held since 2012 and are home to an estimated 250,000 residents living under government siege.
The Syrian Observatory for Human Rights says it is "a large-scale land offensive supported by Russian air strikes aimed at taking bit by bit the eastern sector of Aleppo and emptying it of its residents".
The attacks include artillery barrages and barrel bombings by helicopters.
- No running water -
On September 24 the UN children's agency UNICEF says nearly two million people have been left without water after regime bombardment damages a pumping station and rebels shut down another in retaliation.
- Diplomatic war of words -
Over the next two days the offensive prompts a chorus of diplomatic outrage.
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UN chief Ban Ki-moon says he is "appalled by the chilling military escalation".
"What Russia is sponsoring and doing is not counter-terrorism. It is barbarism," US ambassador Samantha Power tells an emergency meeting of the UN Security Council, while her British and French colleagues accuse Syria and Russia of "war crimes".
Russia riposts by condemning what it called "unacceptable" Western rhetoric.
- Army advance -
On September 27 the army makes its first advance on the ground, taking control of the rebel-held district of Farafira northwest of Aleppo's historic citadel.
A Syrian military official says the offensive to retake Aleppo, with Russian support, involves both air and ground operations, with the use of artillery.
- Hospitals hit -
On September 28, the two largest hospitals in rebel-held parts of Aleppo are hit and forced to suspend activities temporarily. The M10 facility is hit in an air strike and the M2 facility struck by artillery fire, according to the Syrian American Medical Society (SAMS), a US-based non-governmental organisation which supports them.
Ban says attacks on hospitals are "war crimes".
- Prospects for new talks -
US Secretary of State John Kerry warns Russian counterpart Sergei Lavrov that Washington will end talks on the conflict unless Moscow halts the Aleppo assault.
Russia's defence ministry says Moscow is prepared to relaunch talks with the United States on the crisis.
The senior UN official in charge of bringing together the different parties in the Syria conflict, Staffan de Mistura, says there is little prospect of an imminent restart of negotiations "when bombs are falling all over".