National security didn’t play heavily in the presidential election. But President Obama’s legacy, and the country’s future, will be shaped as much by the foreign policy and defense decisions he makes over the next four years as by those on the domestic side.

One of Mr. Obama’s singular contributions has been his vision of a world without nuclear weapons. It is a lofty goal that won’t be achieved in his second term, or maybe for years after that. But it offers a framework for reducing America’s stockpile and for arguing credibly that other countries should follow suit.

In 2010, Mr. Obama won Senate ratification of a treaty with Russia that makes modest cuts in deployed long-range nuclear weapons. It is time to pursue further reductions in those deployed systems, and to seek cuts in warheads held in reserve and in short-range nuclear weapons, where Moscow has a big advantage. Nuclear arms are one area in which the ability of Washington and Moscow to work together is essential. If Mr. Obama can draw the other nuclear powers, including China, Pakistan, India and Israel, into the discussions and persuade the Senate to ratify the Comprehensive Test Ban Treaty, so much the better.

The end of the campaign season might reduce the dangerous partisan posturing over Iran’s nuclear program. Iran and the International Atomic Energy Agency are to resume talks next month, but any diplomatic solution will at some point require direct negotiations between Washington and Tehran. Meanwhile, international sanctions, which have seriously damaged Iran’s economy, need to be rigorously enforced and strengthened.

American military commanders are expected to recommend a timetable soon for withdrawing forces from Afghanistan. After a decade of American blood spilled there, President Obama should declare that the schedule will be dictated only by the security of the troops, and the withdrawal should take no more than a year.

Mr. Obama’s policies have severely weakened Al Qaeda, but extremism is growing in many regions, like North Africa and Pakistan. Dealing with that challenge will likely become harder, as will the choices Mr. Obama must make. For one thing, he will have to examine whether the expanding use of drones is the right approach.

As for the Arab Spring countries, Mr. Obama has been wise to recognize that Washington cannot dictate their democratic evolutions. But he should be more engaged, offering more assistance to Islamic leaders who need to build their economies quickly while reminding them that American support will be calibrated based on their commitment to human rights and the rule of law.

He should continue to resist calls for American military intervention in Syria, but he should search for ways to keep fortifying the opposition in that civil war, especially since the factions there now seem to be unifying.

Many are pessimistic that anything can be done about an Israeli-Palestinian peace deal as long as Prime Minister Benjamin Netanyahu is in office and Palestinians are divided between Fatah and Hamas. It would be a mistake for Mr. Obama to cross this challenge off his list. He needs to keep seeking openings to promote the two-state solution.

Mr. Obama is expected to use his second term to deepen engagement with Asia to protect American military interests and ensure American access to economic opportunities in that region. This could be a challenge given the coming change of leadership in Beijing.

It is an inexhaustible list. Mr. Obama put major new or controversial initiatives on hold this year while the campaign was under way. Now he has two years before another election season impedes his ability to get things done. He needs to decide on his priorities and act while he has the political space and capital to do so.