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. Israel has also sent troops and tanks into the territory.
What is Israel's action in Gaza?
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 armoured vehicles have been seen near Gaza City, on the main road running north to south in the Gaza Strip. Footage verified by the BBC appears to show a tank on the road firing at a car, followed by an explosion.
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 centres, which it has said stretch for 500km (310 miles).
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.