This is what we know about the conflict so far:
How the assault unfolded
Hundreds of Hamas militants attacked Israel from around 6:30 am (0330 GMT) on Saturday, the Jewish holiday of Simchat Torah, in an assault that came 50 years after the outbreak of the 1973 Arab-Israeli war.
The Gaza-based Islamists fired thousands of rockets into Israel and used explosives and bulldozers to break through the fence around the blockaded Palestinian enclave.
Using motorbikes, pickup trucks, motorised gliders and speed boats, the militants streamed into Israel, targeting cities including Ashkelon, Ofakim and Sderot.
The gunmen carried out a massacre at a music festival attended by hundreds of young Israelis and foreigners near Kibbutz Reim, close to Gaza.
Israel said Hamas took more than 150 hostages. They include at least 11 Thais, two Mexicans and an uknown number of Americans and Germans.
How Israel is responding
Israel declared war on Hamas on Sunday, and Defence Minister Yoav Gallant on Monday ordered a “complete siege” on Gaza, meaning “no electricity, no food, no water, no gas”.
The military has massed tens of thousands of troops and heavy armour near Gaza, and called up 300,000 reservists for a campaign it has dubbed “Swords of Iron”.
Netanyahu vowed to reduce to “rubble” the Hamas’s hideouts in Gaza, an impoverished territory of 2.3 million people hemmed in by an Israeli-Egyptian blockade for more than 15 years.
On Tuesday the army said it had “more or less restored control over the border” with Gaza, a day after announcing it was evacuating communities near the frontier.
Israel further pounded Gaza overnight Monday-Tuesday, with strikes concentrated on Jabalia refugee camp.
Hamas’s armed wing, the Ezzedine al-Qassam Brigades, on Monday said Israeli air strikes had killed “four of the enemy’s prisoners”. AFP was unable to verify the claim.
On Tuesday, the journalist syndicate in Gaza said three Palestinian journalists were killed by an Israeli air strike.
There have also been two days of clashes between Israeli forces and Hezbollah in the border area between Lebanon and Israel.
Death toll mounts
Israel says Hamas gunmen have killed more than 900 people and wounded over 2,000 in Israeli cities, towns and kibbutz communities.
AFP journalists have seen the bullet-riddled bodies of civilians on the streets in at least three locations in Israel: Sderot, the nearby kibbutz of Gevim and Zikim beach north of Gaza.
An estimated 270 people were killed at the Supernova music festival near Kibbutz Reim, a volunteer who helped recover the bodies told AFP.
On the Gaza side, health officials said at least 687 people had been killed and more than 2,900 wounded.
On Tuesday, the Israeli military said it had found the bodies of 1,500 Islamist militants in the southern areas that it recaptured.
Eighteen Thais and 10 Nepalis, 11 US citizens and at least eight French nationals are among the foreigners killed from 10 other countries.
Unrest has also broken out in the occupied West Bank where 15 Palestinians have died since Saturday.
What Hamas says about the attack
Hamas said it fired 5,000 rockets in an offensive it branded “Operation Al-Aqsa Flood”.
Its chief Ismail Haniyeh on Saturday vowed to press ahead with “the battle to liberate our land and our prisoners languishing in occupation prisons”.
Hamas has called on “resistance fighters in the West Bank” as well as in “Arab and Islamic nations” to join the battle.
On Monday it ruled out negotiating a prisoner swap with Israel as “the military operation is still ongoing”.
It later threatened to start killing hostages every time Israel launches a strike on a civilian target without warning.
What allies are doing
Lebanon’s Iran-backed Shiite militant group Hezbollah said it launched missiles and artillery shells into northern Israel early Sunday “in solidarity” with the Hamas offensive.
The Israeli army said it retaliated with artillery fire.
On Monday, Israel’s army said it killed a number of armed suspects who crossed the border from Lebanon and that its helicopters carried out strikes in the area.
The United States has vowed “rock solid and unwavering” support for Israel, with President Joe Biden on Sunday ordering “additional support” for its key ally.
The US Navy moved an aircraft carrier battle group to the eastern Mediterranean to boost deterrence against new actors joining the conflict.
In a joint statement released by the White House on Monday, the United States, Britain, France, Germany and Italy condemned the attack and stressed their full support for Israel.
They said they “recognise the legitimate aspirations of the Palestinian people” but said Hamas “offers nothing for the Palestinian people other than more terror and bloodshed”.
Iran has repeatedly denied allegations it had a role in Hamas’ attack, after the Wall Street Journal reported it had helped to plan it and gave the Palestinian group the “green light”.
Supreme leader Ayatollah Ali Khamenei on Tuesday said supporters of Israel were “wrong” to accuse Iran of being behind the Hamas assault.
How the world has reacted
United Nations Secretary-General Antonio Guterres condemned “in the strongest terms” Hamas’s attack on Israel and called for “diplomatic efforts to avoid a wider conflagration”.
He said he was “deeply distressed” by the siege announcement and warned Gaza’s already dire humanitarian situation would “only deteriorate exponentially”.
The European Union on Monday said it was reviewing development aid payments to Palestinians, after a row broke out between member states over suspending payments.
Russia on Monday said creating a Palestinian state was the “most reliable” solution for peace in Israel and that fighting terrorism alone would not ensure security.
Turkish President Recep Tayyip Erdogan, who strongly backs the Palestinian cause, urged both sides “to support peace”.