(CNN) -- Will President Obama talk just about the state of this troubled Union whose economic crisis he has inherited, or will he cast his net of ideas far and wide to address a new American relationship with the world?
Iran's Mahmoud Ahmadinejad has welcomed President Obama's new policies. Will the favor be returned?
Aides say the president is expected to focus on the economy when he addresses a joint session of Congress Tuesday evening, but will also touch lightly on foreign policy issues.
After much talk of engaging America's adversaries, chief among them Iran, the Obama administration has made no move so far, pending a policy review.
But Iranian leaders from President Ahmadinejad on down have sent letters and delivered speeches welcoming a change of U.S. policy and declaring themselves to be ready for talks, 30 years after relations were ruptured by the Islamic revolution.
Iran's help in Iraq and Afghanistan could be useful, though its uranium enrichment program proceeds apace.
But the International Atomic Energy Agency, the United Nations' nuclear watchdog, says Iran seems to be slowing down its centrifuge operations, perhaps as a political gesture of good will.
If Iran is slowly unclenching its fist, will Obama offer an outstretched hand Tuesday night? Watch the speech live at 9 p.m. ET on CNN and CNN.com Live
Facing a two-front war that the Obama administration now calls AFPAK -- for Afghanistan and Pakistan -- will the president define a strategy for winning?
He has already announced 17,000 more U.S. troops for Afghanistan but seems to be pulling back from a promise to help rebuild Afghanistan and promote democracy there.
Meantime, as the United States steadily loses hearts and minds in airstrikes that kill too many civilians, the Taliban is steadily growing stronger in Afghanistan. Across the border in Pakistan too the Taliban is gathering strength, threatening stability there as well as the U.S. ability to resupply its troops in Afghanistan.
Will Obama lay out how he will help Pakistan's new civilian government properly take on the Taliban and al Qaeda militants?
While promising to make Middle East peace a top priority, the president now faces a new dilemma, as Israel's recent elections look set to return Likud leader Benjamin Netanyahu to power if he can put together a coalition.
Netanyahu and his right-wing allies could be on a collision course with the Obama administration, as they reject the idea of negotiations to create a Palestinian state and threaten to build more Israeli settlements on occupied Palestinian land, which violates U.S. policy.
Will Obama lay down the administration's red lines for his road map for peace?
And then there is Russia. Vice President Joe Biden has already called for "resetting the button" on U.S.-Russia relations, which were badly strained between Presidents Bush and Putin. iReport.com: What do you want to hear from Obama?
The new president, Dmitry Medvedev, seems to be pushing back against some of Putin's policies, and there are reports of a possible U.S.-Russia minisummit in April.
Still, issues such as U.S. plans for a missile defense shield in Eastern Europe continue to strain relations with Russia.
Obama's secretary of state has already taken his message on the road to China and elsewhere in Asia, and special envoys have also been deployed. But on April Fool's Day, President Obama himself sets off on his maiden voyage to the world stage.
It will be to London for the G-20 summit, where he'll meet leaders from Europe to Russia to Saudi Arabia.
With Tuesday's speech coming about a month ahead of that trip, allies around the world will hope to hear Obama outline a return to the relationship of consultation, cooperation and compromise.