Israel's ground offensive in Lebanon is the latest cross-border operation in a half-century history of tensions with foes in its northern neighbour:
1978: Operation Litani
Israel made its first incursion into Lebanon when its army invaded part of the country's south from March 14 to 21, 1978.
"Operation Litani" was condemned by the United Nations, which called on Israel to withdraw its forces from Lebanese territory -- a withdrawal Israel would only finally complete 22 years later on June 16, 2000.
Israeli troops entered up to 40 kilometres (25 miles) beyond the border in a bid to push the Palestine Liberation Organisation (PLO) beyond the Litani River and force them to retreat towards Saida or Beirut.
The UN Security Council unanimously passed Resolution 425 on March 19, which established the United Nations Interim Force (UNIFIL) still in operation today.
But after the Israeli army's formal withdrawal Israel indirectly occupied 700 square kilometres by establishing Lebanese proxy militias to maintain control of the area.
Tens of thousands of Lebanese refugees fled to the southern suburbs of Beirut, which then became Hezbollah's bastion.
1982: 18-year-long invasion
On June 6, 1982, the Israeli army returned in a wider-ranging operation it dubbed "Peace for Galilee".
Attempting to root out the PLO from Beirut and end deadly raids by Palestinian fighters on Israel, Israeli soldiers laid siege to the Lebanese capital.
By the end of 1982 nearly 20,000 had died and 30,000 more were injured in the invasion, according to Lebanese authorities. Those include the mainly Palestinian refugee or Lebanese Shia victims of the Sabra and Shatila massacre, perpetrated by Lebanese Christian militias backed by Israel.
Between the end of August and the beginning of September, PLO leader Yasser Arafat and more than 11,000 Palestinian fighters left Lebanon under international supervision.
Hezbollah, the self-described "Party of God", was born in the east of the country after the intervention, with its Shiite militants supervised by the Iranian Revolutionary Guards.
Emerging from the shadows in 1985, the movement quickly established itself and its armed wing, the Islamic Resistance in Lebanon, as a significant thorn for Israel, carrying out suicide attacks and car bombings.
In May 2000, after losing 1,000 troops without being able to eliminate the Iran-backed militants, Israel unilaterally decided to finally withdraw its troops from the country.
2006: 33-day war
Since that withdrawal, a series of violent episodes between Hezbollah and Israel came to a head with the 2006 war, following the kidnapping of two Israeli soldiers on the border.
Israel launched a vast offensive in mid-2006, but the militants stood firm, with Hezbollah's powerful leader Hassan Nasrallah proclaiming a "divine victory".
Lasting 33 days, the war resulted in the deaths of 1,200 Lebanese, mainly civilians, and 160 Israelis, mostly soldiers.
UN Security Council Resolution 1701, which ended the war, stipulated that only the Lebanese army and UN peacekeepers should be deployed in southern Lebanon.
It also called for "the immediate cessation by Hezbollah of all attacks and the immediate cessation by Israel of all offensive military operations".
But Israel accuses the "Party of God" of maintaining its presence in the region, where experts say it has a major network of tunnels.
Hezbollah's main institutions are based in the southern suburbs of Beirut.
The movement has also strengthened its arsenal, which includes guided missiles, and claimed to have 100,000 fighters.
2023-2024: a new showdown
The day after Hamas -- also backed by Iran -- began the Gaza war with its October 7 attack on Israel, Hezbollah and Israel began low-level artillery exchanges. Hezbollah said it was acting in support of its Palestinian allies.
After a year of hostilities which forced around 60,000 Israelis to flee the north, the Israeli army launched a deadly bombing campaign targeting southern Lebanon and Beirut.
A few days earlier, a wave of explosions of pagers and walkie-talkies used by Hezbollah members left dozens dead and thousands injured in Lebanon in an operation widely blamed on Israel.
Israel, which said it is acting to stop Hezbollah firing at the country's north, claims to have killed most of Hezbollah's senior leaders in recent months.
The death on Friday of Nasrallah in a strike on southern Beirut, represented a major blow to Hezbollah and a significant victory for Israel against its arch-foe Iran.
On Monday evening, the Israeli army announced that it had put troops on the ground to fight Hezbollah in villages in southern Lebanon, despite international calls for de-escalation.
Israel insisted these were "limited, localised and targeted raids" against Hezbollah and its infrastructure.
Since mid-September, the death toll from Israeli strikes in Lebanon has risen to more than 1,000, according to the country's health ministry, while hundreds of thousands of people have been displaced.