Here is a rundown of what is known about Israel's ground operation so far.

- When did the offensive begin?

Late Monday, Israel's military began what it called "limited, localised and targeted raids" against Hezbollah in southern Lebanon's border areas.

Its ground forces are backed by fighter jets and artillery fire.

The military formally announced the start of the ground offensive hours after the United States said Israeli forces were conducting limited operations in Lebanon.

The military did not reveal how many soldiers were involved in the incursion, but said its 98th division -- including paratroopers and commando units -- was taking part.

The division had been previously deployed in the Gaza Strip, where Israeli forces continue to battle Palestinian militants led by Hamas.

On Monday evening, the military declared three areas along the northern border with Lebanon a "closed military zone", providing the first indication of a possible ground offensive.

- What are Israel's targets? -

The military said it was acting on "precise intelligence" targeting Hezbollah positions and infrastructure in southern Lebanon.

"These targets are located in villages close to the border and pose an immediate threat to Israeli communities in northern Israel," it said.

The ground assault comes after Israeli air strikes killed several top Hezbollah commanders in recent weeks, including Nasrallah on Friday.

"The elimination of Nasrallah is an important step, but it is not the final one," Defence Minister Yoav Gallant warned on Monday, hours before the offensive was announced.

"We will use all the means that may be required -- your forces, other forces, from the air, from the sea, and on land," Gallant told soldiers in the north.

- What are Israel's goals? -

Since October 8, Hezbollah has been firing rockets from across the border, displacing more than 60,000 residents in northern Israel.

Hezbollah has said it was acting in solidarity with its Islamist ally Hamas in Gaza, following the unprecedented attack on Israel on October 7 that resulted in the deaths of 1,205 people on the Israeli side, according to an AFP tally based on Israeli figures.

The ensuing cross-border clashes have intensified in recent weeks.

While Israel engaged in fierce fighting with Hamas in Gaza, Gallant announced on September 18 that the "centre of gravity" of the war was now pivoting to the north.

"It was now time to ensure that those displaced from the north would be able to return to their homes," he said.

Other officials including Prime Minister Benjamin Netanyahu have repeatedly vowed to return those displaced back to their homes.

"We will continue to hit Hezbollah... the one who has a missile in his living room and a rocket in his home will not have a home," Netanyahu said in a statement last month.

- How has Hezbollah responded? -

Since the ground offensive began, Hezbollah has fired several rockets into Israel, with explosions heard in the commercial city of Tel Aviv on Tuesday.

A statement said it had "launched salvoes of Fadi 4 rockets at the Glilot base of the military intelligence's unit 8200 and the Mossad headquarters located on the outskirts of Tel Aviv".

Hezbollah said it also targeted Israeli troop movements in Metula in northern Israel "with artillery shells" and later a "gathering of enemy soldiers" in the same area with rockets.

Israeli troops in northern Israel's Avivim were also targeted, the group added.