Global leaders are descending on the U.N. Headquarters in New York City this week for the U.N. General Assembly.

Starting Monday, the 70th edition of the gathering will mix together a dizzying array of international allies and rivals -- with uncertain results.

Here's what you need to keep your eye on this week:

SPEECH-A-PALOOZA

World leaders step up to the mic

The assembly's general debate sessions are always packed with a daunting amount of speeches. But Monday has a music festival lineup's worth of presidential heavy hitters . You've got Obama, you've got Putin, you've got Xi Jinping of China, Hassan Rouhani of Iran and a ton of other leaders. Not forgetting U.N. Secretary-General Ban Ki-moon, of course, who'll kick off proceedings. They'll all probably have their own take on what ails the world and what can cure it. Climate change and the widening impact of the relentless war in Syria are likely to be prominent themes.

BEHIND CLOSED DOORS

Obama and Putin come face to face

Beyond the grandstanding at the podium, the real geopolitical maneuvering takes place later Monday when Obama and Putin talk face to face on the sidelines. It's the first meeting between the two world leaders in more than 10 months; the previous occasion was a frosty encounter at the G20 summit in Australia last year. The tension will no doubt be cut-with-a-knife thick once again. This time around, it's not just Russian involvement in the Ukrainian conflict souring the mood -- Obama is also concerned about poker-faced Putin's recent military moves in war-ravaged Syria

(I)RANTS AND RAVES

Iranian leader mocks U.S. Republicans

President Rouhani will address the audience after the likes of Obama, Xi and Putin have had their say. His speech will be picked over for his tone on the landmark agreement reached on Iran's nuclear program in July. This is Rouhani's first visit to the U.S. since then, and he appeared in a jovial mood Sunday discussing Republican presidential candidates' attacks on the deal with CNN. "Some of it was quite laughable. It was very strange, the things that they spoke of," he said, suggesting some of the candidates could hardly find Iran on a map. His country's bitter regional rivalry with Saudi Arabia is also in focus after the two sides traded barbs over last week's deadly stampede during the Hajj pilgrimage near Mecca.

NEW KID ON THE BLOCK

Cuban President follows in his brother's footsteps

Raul Castro last visited the United States more than half a century ago. Back in 1959, he and his brother Fidel received a warm welcome in Houston . But after that, U.S.-Cuban relations quickly went south (Bay of Pigs, Cuban Missile Crisis etc.). After decades of bad blood, the two sides restored diplomatic ties in July. Now, Raul is set to make his debut at the General Assembly, and he has a tough act to follow. Fidel, his big brother and presidential predecessor, holds the record for the longest timed speech ever delivered to the world gathering, clocking up a vocal-chord-straining address of 4 hours and 29 minutes in 1960. Let's hope Raul can be less long-winded on Monday afternoon when he's expected to cover issues like efforts to remove the ongoing U.S. trade embargo on Cuba.

RIPE WITH SYMBOLISM

The raising of the Palestinian flag