William J. Burns, the C.I.A. director, landed in Qatar on Wednesday to try to advance a deal between Israel and Hamas to finally end the war in Gaza and free the remaining hostages held there, amid rising optimism that an agreement could be coming together after months of fruitless negotiations.

Officials from countries involved in the talks say the two sides could be nearing a truce in the war that began with the Hamas-led attacks on Israel on Oct. 7, 2023. A senior U.S. official and another official familiar with the matter confirmed the visit by Mr. Burns, who has been the lead American negotiator, but like others spoke on condition of anonymity to discuss the sensitive diplomacy.

Over months of negotiations, hopes for a breakthrough have risen and fallen, each time with Israel and Hamas blaming each other for the impasse. If an agreement is reached, it would be the first pause in the fighting since November 2023, when the two sides observed a weeklong truce that saw the release of 105 hostages from Gaza and some 240 Palestinian prisoners in Israel.

But another official briefed on the matter cautioned that major hurdles remained in the talks, and noted that Mr. Burns was expected to meet this time only with officials from Qatar, not those from Egypt or Israel, the other major players in the discussions.

Here’s what we know so far about the latest talks:

In a change from previous negotiations, both sides have generally refrained from leaking the details of the talks to the media. Some analysts said they believed the blackout indicated that Israel and Hamas were more serious about an accord this time around.

Calls for school crackdowns have mounted with reports of cyberbullying among adolescents and studies indicating that smartphones, which offer round-the-clock distraction and social media access, have hindered academic instruction and the mental health of children.

According to officials familiar with the talks, mediators have floated a cease-fire beginning with a 60-day truce. During this phase, Hamas would release some of the 100 or so hostages still held in Gaza — some of them dead — in exchange for Palestinians jailed in Israel.

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