On Sunday, traffic began flowing freely in Egypt's Tahrir Square for the first time in three weeks. As schools and businesses re-opened, the country's revolutionary fervor began to subside. Still, most of the demands of protesters have not been met. And the longer these problems fester, the greater the risk of renewed protests and instability. Here are the biggest challenges the Egyptian military faces in the coming months.

Rewriting the Constitution  Egypt's old constitution imposed a number of "built-in guarantees" that ensured former President Hosni Mubarak's grip on power and tilted elections in his party's favor. It also prevented a number of opposition groups, including the Muslim Brotherhood, from participating in elections. Now, in a communique read on state TV, the Supreme Council of the Armed forces has promised to appoint a committee to rewrite the constitution and put the changes to a vote. "The hard part," explains Steven Taylor at Outside the Beltway, will be "figuring out who to invite to the table" during the negotiating process.

Elections  Giving a vague timeline, the military said in a statement it would "manage the affairs of the country for a temporary period of six months or until the end of elections to the upper and lower houses of parliament, and presidential elections." As Reuters's Marwa Awad and Dina Zayed explain, the election will be "complex process." The military's intentions of keeping military rule for six months suggests that elections should occur sometime between then and now.

Communicating a Game Plan  According to CNN, leading opposition figures are demanding clear, detailed plans on how the military will transition Egypt into a democracy. "They need to come out of their headquarters and start talking to the people and tell us what is in store for us," Mohamed ElBaradei told CNN. Urging the government to move quickly, activist Wael Ghonim said the "biggest mistake now is to give the Egyptian people too little too slow. Restoring confidence requires a faster pace."

Disentangling the Military's Grip on the Economy  As Time's Aryn Baker explains, "soldiers staff military-owned companies that produce everything from olive oil to washing machines, televisions, cement and even the ubiquitous Safi brand of bottled water. The military owns land, operates hotels and runs construction companies. Retired generals are often offered lucrative positions on the boards of private companies." This deep entrenchment into the workings of society is troubling, Baker says, because both Egypt's defense minister, Mohamed Hussein Tantawi, and the military chief of staff, Lieut. General Sami Hafex Enan, are "vestiges of the old regimes." Baker quotes a professor of international relations at the London School of Economics who says "Tantawi is as conservative as Mubarak, and he doesn't believe in economic or structural change ... He doesn't believe that Egyptians are ready for democracy."

Job Creation  "Political unrest is virtually certain to flare up again if the ruling military council fails to create new jobs and kick-start the country's moribund economy," writes Yochi Dreazen at National Journal. (In fact, some economy-related protests are already surfacing).  He cites a report saying that Egypt's youth are being hit disproportionately by the country's high unemployment rate, though nearly 900,000 of them holding university degrees. One of the ways of combating unemployment is to "privatize the military's business holdings," which Dreazen says "extend into virtually every aspect of daily life." Unfortunately, whenever this was attempted during Mubarak's reign, the military resisted such reforms, seeing them as a threat to its economic health. The military will have to make concessions in that respect if unemployment is to be assuaged, argues Dreazen.