3. How big a threat do the Taliban still pose?
The Taliban are still "resilient and determined," according to a recent Pentagon report, and pose a major security threat.
The Taliban continue to carry out high-profile attacks in the capital, Kabul, even targeting the Afghan Supreme Court during a suicide attack in June. Another strike targeted a building near Kabul airport.
On Tuesday, a suicide bomber attacked the convoy of Haji Mohammad Mohaqiq, a member of parliament, killing three people and wounding 21 others. Three bodyguards were among the injured. Mohaqiq -- a Shiite and an ethnic Hazara -- is a member of Afghanistan's political opposition.
The Taliban regime in Afghanistan was sheltering al Qaeda when the terror network launched attacks against the United States on September 11, 2001. The next month, the United States cranked up military operations that led to the toppling of the Taliban government.
Ever since, international forces have been fighting radical Islamic militants in Afghanistan and neighboring Pakistan.
4. What are the biggest challenges?
The main fear among Afghans is that the country could revert to another civil war once the United States withdraws its combat troops.
"Some people we've spoken to sort of take it for granted that there's going to be a civil war when the United States leaves," said CNN's Erin Burnett on a trip last year to Afghanistan. "It happened before when the Soviet Union left (in 1989)."
Above all, Karzai said the Afghan army needs the tools to battle the insurgents, namely more equipment and firepower. He came to the Pentagon in January with a wish list asking for more helicopters, drones and other hardware, according to a senior defense official.
"We need an air force. We need air mobility," Karzai told Amanpour. "We need proper mechanized forces. We need, you know, armored vehicles and tanks and all that."
Retired Army Gen. Stanley McChrystal, once America's top commander in Afghanistan, said the Afghan people are "terrified because they think they have something to lose."
"There has been progress made," he said. "But they're afraid that if we completely abandon them in 2014, as they perceive we did in 1989, (things) would all go back."
5. What support will the United States and allies provide?
American forces, now at about 66,000, are expected to dip to 32,000 by the end of the year and further throughout 2014.
The plan is to withdraw all combat troops but keep a residual force in the country to help train Afghans and carry out counterterrorism operations when needed.
The size of that force is still being discussed.
Gen. John Allen, the former commander of U.S. troops in Afghanistan, recommended between 6,000 and 15,000 troops. But that figure was lowered to a range between 2,500 and 9,000, according to a defense official.
The United States and NATO have pledged to continue to support and train Afghan forces in what NATO Secretary-General Anders Fogh Rasmussen deems a "new relationship," starting in 2015.
Acknowledging that there is still much to do in the interim 18 months, Rasmussen said, "Today, our shared goal is in sight."