Lightning Strike: Israel opened its offensive with a surprise airstrike on Nov. 14 that killed the shadowy leader of Hamas’ military wing. Since then, it has carried out hundreds of airstrikes in what it says is a systematic campaign to halt years of rocket attacks launched from Gaza. While Israel claims to have inflicted heavy damage, dozens of rockets have continued to fly out of Gaza each day.

Why Now? Israel launched the operation in response to days of rocket attacks out of Gaza, highlighted by a rare missile strike on an Israeli military jeep that wounded four soldiers. But the operation was actually years in the making. Since a previous Israeli offensive four years ago, Hamas has restocked its arsenal with more sophisticated and powerful weapons smuggled in from Egypt through underground tunnels. After a lull following Israel’s previous offensive, rocket fire has steadily climbed the past two years. The Israeli military says more than 700 rockets were launched into Israel this year before it launched the offensive last week. In this environment, Israeli officials have said it was only a matter of time before a new round of fighting broke out.

The battlefield: Hamas seized control of Gaza, a densely populated strip of land sandwiched between southern Israel and Egypt’s Sinai desert, five years ago from the rival Fatah movement of Palestinian President Mahmoud Abbas. Hamas, a militant group sworn to Israel’s destruction, has developed is rocket arsenal to the point where nearly half of Israel’s population is in range.

Why Fire Rockets? Palestinian militants, led by Hamas, say the rocket fire is a legitimate response to continued Israeli attacks. They also claim they are resisting Israeli occupation of the territory. Israel withdrew from Gazain 2005, ending a 38-year military occupation. But it has maintained a blockade of the territory in a step it says is needed to prevent arms smuggling. In the murky world of Gaza politics, the attacks also stem from internal rivalries between groups eager to prove their militant credentials. Israeli Prime Minister Benjamin Netanyahu says no country would tolerate repeated missile attacks on its civilians.

Risky Business: Prolonged fighting carries great risks for both sides. As Israel presses forward, the number of Palestinian civilian casualties is likely to rise — a scenario that could quickly turn international opinion against it. Israel’s previous offensive left hundreds of civilians dead, drawing international condemnation and war crimes accusations. By continuing to fire rockets, Hamas raises the risk of tougher Israeli attacks, including a possible ground offensive. Well aware of these risks, both sides are working through mediators to arrange a cease-fire.

Terms of the Deal: Israel wants a halt to the rocket attacks and an end to arms smuggling into Gaza, most likely in a deal that is guaranteed by Egypt or other international parties. Hamas wants a halt to Israeli assassinations of its leaders and a lifting of the Israeli blockade. While gaps remain wide, both sides have strong interests in a deal. Bringing quiet to Israel’s embattled south will make Netanyahu a national hero, weeks before parliamentary elections. Hamas, branded a terrorist group by Israel and the West, has seen its influence grow as the Arab Spring brings Islamists to power across the region. A cease-fire, particularly an arrangement guaranteed with international partners, would cement Hamas’ control of Gaza and give it more of the international recognition it covets so much.

By the numbers:

—More than 100 Palestinians, half of them civilians, have been killed, according to Palestinian medical officials. Three Israeli civilians have died from rocket fire.

—Israel has attacked more than 1,350 targets in the current offensive, according to the Israeli army. Hamas and smaller armed groups have responded with nearly 600 rockets, the army says.

—Israel says its new “Iron Dome” rocket-defense system has shot down more than 300 incoming projectiles.