Explained | All you need to know about Israel's peace talks in Gaza and Lebanon

Ceasefire talks are underway to resolve two related conflicts in West Asia that have killed tens of thousands of people and threaten to spiral into a wider regional war.

On Thursday, top US officials held talks in Egypt and Israel in an attempt to end the conflicts between Israel and Hamas in the Gaza Strip, and between Israel and Hezbollah in Lebanon. Envoys from Israel, Egypt, the United States and Qatar also met in Doha, the Qatari capital, on Oct. 28.

Since the October 7, 2023, attacks by Hamas in which about 1,200 people in Israel were killed and about 250 were taken hostage, more than 43,000 Palestinians have been killed in Gaza and nearly 3,000 people have been killed in Lebanon, according to local health ministries, which do not distinguish between civilians and combatants.

Here's what to know about the key players, negotiations and major obstacles.

Israel-Hamas

Who are the players?

Qatar and Egypt mediate on behalf of Hamas, which does not directly participate in the talks. Mohammed bin Abdulrahman Al Thani, the prime minister of Qatar, has been deeply engaged in the talks. Gen. Abbas Kamel, was Egypt's top cease-fire negotiator, but he was removed recently from his post as intelligence chief, leaving his role in the talks unclear. Egyptian President Abdel Fattah el-Sissi has also been involved in negotiations.

The chief of Israel's Mossad foreign intelligence service, David Barnea, is one of his country's primary negotiators, along with Ronen Bar, head of the Shin Bet, the domestic security service, and Nitzan Alon, a top military general.

CIA Director William Burns is playing a lead role for the US in talks, along with the White House's Middle East coordinator, Brett McGurk.

What are they negotiating?

The central idea behind the cease-fire is that fighting in Gaza between Israel and Hamas would stop, the Israeli military would withdraw from the enclave, and Hamas would release the roughly 100 hostages remaining in Gaza in exchange for Palestinian prisoners jailed in Israel.

In October, mediators floated a separate short-term proposal: a temporary truce and the release of a few Israeli hostages in exchange for some Palestinians imprisoned in Israel. That proposal included a humanitarian aid component to address severe shortages of food, medicine and critical supplies in Gaza. That could pave the way for a more comprehensive deal.

Multiple versions of the short-term proposal are still under discussion. One would release female hostages along with male captives older than 50 in return for a set number of Palestinian prisoners, according to a person briefed on the discussions, who spoke on the condition of anonymity. In another version, Hamas would release four hostages over roughly 10 days, according to a second official briefed on the negotiations.

What are the biggest obstacles?

The specifics are where everything gets tricky: the terms, timeline and details of an Israeli withdrawal; who would be in charge in the enclave after Israel's withdrawal; and the details of the hostage-for-prisoner exchange.

Hamas insists that Israel commit to a full and permanent withdrawal of its military from Gaza. Israeli Prime Minister Benjamin Netanyahu says his country must maintain control of an 8-mile-long stretch of Gaza near Egypt, known to Israelis as the Philadelphi corridor, to ensure Hamas can no longer smuggle arms.

Hamas has rejected the scaled-down proposal that emerged from weekend discussions in Qatar, signaling that the impasse will be hard to break.

Israel also wants the option of resuming military operations in Gaza after a temporary halt in fighting; Netanyahu says Israel must wipe out Hamas as a fighting or governing force. That fundamentally contradicts Hamas' premise that a cease-fire would end the war and permanently remove the Israeli military from Gaza.

What are the latest developments?

Burns met with officials in Cairo on Thursday, including el-Sissi. McGurk and Amos Hochstein, President Joe Biden's de facto envoy on the conflict with Hezbollah in Lebanon, held talks in Israel with Netanyahu and Yoav Gallant, the Israeli defense minister.

Negotiators had initially hoped that Hamas would be more willing to negotiate after Israel in October killed its leader, Yahya Sinwar, but have since said there has been no indication that the armed group's stance has changed.

Among the crucial developments is one that has yet to happen -- the US presidential election. Netanyahu sees an advantage in delaying the negotiation process, according to some Israeli officials familiar with his thinking, under the assumption that Israel will receive more US support if Donald Trump regains the presidency.

Israel-Hezbollah

Who are the players?

Hezbollah's leader as of late October is Sheikh Naim Kassem, who took over after an Israeli airstrike killed the group's longtime chief, Hassan Nasrallah. Kassem has signaled some openness to a cease-fire.

Kassem has said he is in communication with Nabih Berri, speaker of Lebanon's parliament, who has long been a key intermediary between the United States and Hezbollah.

Lebanese Prime Minister Najib Mikati is engaged in negotiations with international mediators.

Hochstein, an Israeli-born US energy policy official who became a key White House envoy on the conflict, trades messages with Hezbollah via Berri. Hezbollah has been designated a terrorist organization by the US, so US officials are barred from speaking with it directly.

Hochstein and McGurk met with a number of Israeli officials on issues including Lebanon in the past week. Israeli officials are not negotiating directly with their Lebanese counterparts. Hochstein, serving as a mediator, primarily engages with Netanyahu and Gallant about the situation in Lebanon.

While the talks about the conflict in Lebanon are taking a separate track from discussions about Gaza, there is some overlap among participants in the two sets of negotiations.

What are they negotiating?

Israel is conducting a ground war in southern Lebanon and carrying out airstrikes throughout the country. Its stated goal is to clear out Hezbollah's forces from southern Lebanon, to enable about 60,000 people to return to their homes in northern Israel, without fear of Hezbollah rocket barrages.

The Lebanese government is calling for the revival of a 2006 cease-fire plan outlined in UN Security Council Resolution 1701, which unsuccessfully tried to create a buffer zone between Israel's northern border and Lebanon's Litani River, policed by UN peacekeepers and the Lebanese national army.

Hezbollah has said it will not stop fighting until Israel withdraws from Gaza, but in a speech in late October, its new leader, Kassem, suggested the group would be open to an agreement under "suitable" conditions, while pledging that it was also prepared to keep fighting a protracted conflict.

What are the biggest obstacles?

Resolution 1701 failed. Hezbollah did not disarm or withdraw from southern Lebanon, and instead built up its arsenal to become the best-armed militia in the world.

The Lebanese army is not in a position to control Hezbollah, which is a major player in Lebanon's national government, and the UN peacekeepers were not empowered to do so. So it is unclear what would be needed to enable them to police a potential buffer zone in southern Lebanon.

Hezbollah has said its presence in the demilitarized zone is justified because Israel did not keep its commitment to withdraw completely from Lebanon. The United Nations assessed that Israel did withdraw. Hezbollah bases its claim on land known as the Shebaa Farms, which Israel contends is part of the Golan Heights captured from Syria in the 1967 war, and not a part of Lebanon.

Israel wants any cease-fire deal to explicitly state that it can invade Lebanon again if the terms of an agreement are violated. That insistence has been a major sticking point in the negotiations.