The offensive followed an announcement by a US-led coalition fighting the Islamic State group that it would create a thousands-strong border force in northern Syria.
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Around half of that force would be retrained fighters from the US-backed Syrian Democratic Forces, which is mainly made up of fighters from the Syrian Kurdish People's Protection Units (YPG) militia.
Here is a timeline of the main events since:
Major incursion
On January 20, Turkey launches operation "Olive Branch" into Syria, aiming to oust the YPG militia from its enclave of Afrin.
War planes and artillery back a major ground incursion including Ankara-backed Syrian rebels.
Turkey considers the YPG to be a "terrorist" group and the Syrian offshoot of the Kurdistan Workers' Party (PKK) which has waged a bloody three-decade insurgency against the Turkish state.
Syrian President Bashar al-Assad condemns "brutal Turkish aggression".
Assad ally Russia withdraws troops from the zone in question "to prevent potential provocation".
The Kurdish militia say they will hold Russia as well as Turkey responsible for the attacks.
'Legitimate' concerns
On January 21, Turkish tanks and soldiers enter the Afrin region.
Ankara says it aims to create a security zone 30 kilometres (18 miles) deep inside Syria.
The US State Department calls on Turkey to "exercise restraint", but Defense Secretary Jim Mattis says Ankara has "legitimate" security concerns and had warned Washington prior to the operation.
'Agreement' with Russia
"We spoke about this with our Russian friends. We have an agreement," Turkish President Recep Tayyip Erdogan says on January 22.
Kurdish forces urge their Western allies to act, saying Turkey's operation amounts to support for IS.
On January 24, rockets are launched from Syria at the Turkish border town of Kilis. Turkish forces respond with artillery fire.
US-Turkey tensions
In a telephone call with Erdogan, US President Donald Trump urges Turkey "to de-escalate, limit its military actions" and "avoid any actions that might risk conflict between Turkish and American forces", according to the White House.
However, on January 25 Turkish official sources dispute the American account of the conversation, saying Trump did not share any concerns regarding "escalating violence".
On January 26, Erdogan threatens to expand Turkey's offensive in Syria, vowing to "clean up" the YPG-held northern city of Manbij, where the US has a military presence.
On February 16, the US and Turkey agree to "work together", notably in Manbij.
Turkish army enters Afrin
On February 20-21, pro-regime forces enter Afrin, only to come under fire from Turkish forces.
Turkey says it will consider a "legitimate target" any group that comes to the aid of Kurdish militia in Afrin.
On February 26, it sends special forces into Afrin in anticipation of a "new fight".
On March 8, Turkish forces and allied Syrian rebels take control of the key northern town of Jandairis from the Kurdish militia.
"Today we are in Afrin and tomorrow we will be in Manbij. And the next day we will ensure that terrorists are cleared east of the Euphrates River up to the Iraqi border," Erdogan says.
On March 18, Turkish forces and their rebel allies take control of Afrin. More than 1,500 Kurdish combattants have been killed over the past two months, according to the Syrian Observatory for Human Rights monitor.
Erdogan says Turkish rebels have taken "total" control of the centre of Afrin.
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