Hamas gunmen launched an unprecedented assault on Israel from the Gaza Strip on 7 October, killing more than 1,400 people and taking at least 239 hostages.
Since then, Israel has been carrying out retaliatory strikes on Gaza, in which more than 8,000 people have been killed, according to the Hamas-run health ministry in Gaza. Israel has also sent troops and tanks into the territory.
Israel’s Prime Minister, Benjamin Netanyahu, said ground forces had gone into Gaza to “dismantle” Hamas and bring hostages home.
On Monday, the Israel Defense Forces (IDF) said its troops had “killed dozens of terrorists who barricaded themselves in buildings and tunnels and attempted to attack the troops”.
The IDF said it had continued to strike hundreds of Hamas targets from the air.
It said that in one attack, an aircraft was guided by forces on the ground and struck a building “with over 20 Hamas terrorist operatives inside it”.
A fighter jet also struck a military post used to launch anti-tank missiles near Al-Azhar University in northern Gaza, the IDF added.
Israeli armored vehicles have been seen near Gaza City, on the main road running north to south in the Gaza Strip.
The Palestinian Red Crescent said the Israeli military issued an evacuation order for Al-Quds hospital in northern Gaza but that it was impossible to move hundreds of the patients who are being treated there.
Eyewitnesses have described heavy shelling around the hospital, where 14,000 people are thought to be sheltering.
The Israeli military has massed tens of thousands of soldiers along Gaza’s perimeter fence, along with tanks and artillery. It has activated some 300,000 reservists alongside its standing force of 160,000.
Hamas is thought to have about 25,000 members in its military wing. It also has a network of underground tunnels across Gaza, connecting its command centers, which it has said stretch for 500km (310 miles).
Why is this happening now?
On 7 October, hundreds of Hamas gunmen crossed from the Gaza Strip into southern Israel by breaking through the heavily fortified perimeter fence, landing by sea, and using paragliders.
It was the most serious cross-border attack Israel has faced in more than a generation.
The gunmen killed 1,400 people, most of them civilians, in a series of raids on military posts, kibbutzim and a music festival and took hostages back into Gaza And Israel War.
Mr Netanyahu said after the attack that Israel was at war and vowed that Hamas would “pay an unprecedented price“.
Given the resources of Israel’s security services, it was astounding that the attack by Hamas was not anticipated, the BBC’s security correspondent Frank Gardner says.
It came at a time of soaring Israeli-Palestinian tensions.
This year has been the deadliest on record for Palestinians who live in the Israeli-occupied West Bank, which could have motivated Hamas to strike Israel.
Hamas might also have been seeking to score a significant propaganda victory to boost its popularity among ordinary Palestinians.
The capture of Israeli hostages is thought to be designed to pressure Israel to free some of the estimated 4,500 Palestinians held in Israeli prisons.
The Israeli military says 229 people are still being held in Gaza.
They include 20 children and at least ten people aged over 60. Soldiers were also taken hostage.
Hamas has so far returned four hostages, with the Gulf state of Qatar acting as a mediator for their release.
What is the Gaza Strip, and who lives there?
The Gaza Strip is a 41 km (25-mile) long and 10 km-wide territory located between Israel, Egypt and the Mediterranean Sea.
Originally occupied by Egypt, Gaza was captured by Israel during the 1967 Six-Day War.
Israel withdrew its troops and around 7,000 settlers from the territory in 2005.
It is home to 2.23 million people and has one of the highest population densities in the world.
Just over 75% of Gaza’s population – some 1.7 million people – are registered refugees or descendants of refugees, according to the UN. More than 500,000 of them live in eight crowded camps located across the Strip.
Israel controls the airspace over Gaza and its shoreline and has strictly controlled the movement of people and goods.
What is Palestine?
The West Bank and Gaza, which are known as the Palestinian territories, as well as East Jerusalem and Israel, all formed part of a land known as Palestine from Roman times until the mid-20th Century.
These were also the lands of Jewish kingdoms in the Bible and are seen by many Jews as their ancient homeland.
Israel was declared a state in 1948, though the land is still referred to as Palestine by those who do not recognize Israel’s right to exist.
Palestinians also use the name Palestine as an umbrella term for the West Bank, Gaza, and East Jerusalem.
The Palestinian president is Mahmoud Abbas, also known as Abu Mazen. He is based in the West Bank, which is under Israeli occupation.
He has been the leader of the Palestinian Authority (PA) since 2005 and represents the Fatah political party, a bitter rival of Hamas.
On Monday, Hamas released a video showing three people held hostage in Gaza. Although BBC News does not know about the conditions under which it was filmed, the three women appear to be in reasonable health with no obvious signs of injury.
What is Hamas, and what does it want?
Hamas is a Palestinian group that has ruled the Gaza Strip since 2007. The group is sworn to Israel’s destruction and wants to replace it with an Islamic state.
Hamas has fought several wars with Israel since it took power. It has fired – or allowed other groups to fire – thousands of rockets into Israel and has carried out other deadly attacks.
In response, Israel has repeatedly attacked Hamas with air strikes. In 2008 and 2014, it also sent troops into Gaza war.
Together with Egypt, Israel has blockaded the Gaza Strip since 2007 for what it describes as security reasons.
Hamas – or in some cases, its military wing, the Izzedine al-Qassam Brigades – has been designated a terrorist group by Israel, the United States, the European Union, and the UK, as well as other powers.