Israel has invaded southern Lebanon in a dramatic escalation of its conflict with Hezbollah.

The Israeli ground operation began on Monday night, days after an air strike killed Hassan Nasrallah, the leader of the Iran-backed armed group.

Hezbollah has fired rockets into northern Israel as Lebanon has endured two weeks of aerial bombardment that Lebanese authorities say has killed more than 1,000 people and forced up to a million to flee their homes.

Israel has a decades-long history of conflict with Hezbollah but the war in Gaza has sparked a year of deadly cross-border fighting between them.

We will be continually updating maps in this page to help explain the conflict.

Lebanon is a small country with a population of about 5.5 million people, which borders Syria to the north and east, Israel to the south, and the Mediterranean Sea to the west. It is about 170km (105 miles) away from Cyprus.

Israeli troops and tanks that had gathered close to the border crossed into Lebanon on Tuesday but it is unclear exactly where they are operating.

The Israel Defense Forces (IDF) has said it is carrying out “limited, localised, and targeted ground raids” in southern Lebanon to dismantle what it calls Hezbollah’s “terrorist infrastructure”.

Israeli troops are fighting directly with Hezbollah fighters on the ground, according to the BBC’s Nick Beake who is in northern Israel.

Several Israeli soldiers have been killed in mortar attacks and ambushes by Hezbollah during operations in southern Lebanon aimed at “eliminating terrorists,” according to the IDF.

Hezbollah said its fighters had clashed with Israeli forces in Adaisseh, Kafr Kila, Maroun al-Ras and Yaroun – all Lebanese villages close to the border with Israel.

A ground operation in southern Lebanon comes with many risks for Israeli forces. Unlike the flat coastal plains of Gaza, southern Lebanon has rolling hills and some mountainous terrain that makes it difficult for tanks to move easily without fear of being ambushed.

Hezbollah is also thought to have a network of tunnels in the region, with the group having been preparing for another full-scale conflict with Israel since the 34-day war in 2006.

As part of its invasion of southern Lebanon, the IDF has ordered people living in some villages to evacuate, telling those remaining to leave their homes and “immediately head to the north of the Awali River” – which meets the coast about 50km (30 miles) from the border with Israel.

Lebanese civilians have also been warned by the IDF not to use vehicles to travel south across the Litani River, located about 30km (20 miles) north of the border.

About a million people lived in southern Lebanon before the conflict escalated almost a year ago.

Tens of thousands have been fleeing north since Israeli air strikes in the region intensified in late September. The main route for civilians trying to leave the south is the coastal road that runs the length of the country – but areas along that route have been hit by air strikes in recent days.

Israel’s invasion of southern Lebanon came after nearly two weeks of intense air strikes that Israel’s military says target Hezbollah in the south of the country, the eastern Bekaa Valley and the southern suburbs of Beirut.

Israel says it is hitting Hezbollah sites, including weapons stores and ammunition dumps, but Lebanese officials say more than 100 women and children have been killed.

The majority of the rockets recently fired by Hezbollah have targeted northern areas of Israel. But some rockets have reached further south and damaged homes near the coastal city of Haifa.

There has been almost a year of cross-border hostilities between Israel’s forces and Hezbollah, sparked by the war in Gaza.

Hezbollah has fired thousands of rockets at northern Israel during that time, forcing some Israelis living there to flee south, while the IDF has launched air strikes and artillery fire against Hezbollah positions in Lebanon.

As the chart below shows, the number of weekly Israeli attacks on Lebanon more than tripled in the week before the IDF launched its ground invasion. The number of Hezbollah attacks, while small in comparison, also increased in the same week.

Israel has intensified strikes on Beirut, the capital of Lebanon, in recent days.

The majority of the strikes have hit Dahieh, a southern suburb of the city that is a densely populated area home to thousands of civilians.

The suburb has a strong Hezbollah presence and a series of Israeli strikes on buildings in the area killed Hezbollah’s leader Hassan Nasrallah on 27 September.

There have also been Israeli aerial attacks on locations closer to the centre of the city. A strike on an apartment block close to the Lebanese parliament building on 2 October killed several people, including rescue officers and paramedics, according to Beirut’s civil defence.

Israel is now engaged in hostilities with armed forces and non-state armed groups in several countries in the Middle East, including Iran, Syria and Iran-backed groups operating in Lebanon, Gaza, Iraq, Syria and Yemen.

Iran’s ballistic missile attack against Israel on Tuesday was the latest major escalation.

What happens next is unclear, but Israel has vowed to respond, with Prime Minister Benjamin Netanyahu describing the attack as “a big mistake” that Iran “will pay for”.