Karzai's two main opponents -- out of 41 people running -- are Abdullah Abdullah and Ashraf Ghani.
The results of the poll are not expected to be known for several weeks. If Karzai fails to win a majority on Thursday, he would enter a run-off with the second-place candidate in early October.
Abdullah Abdullah is an eye doctor who served as foreign minister in Afghanistan's transitional government following the 2001 ouster of the Taliban regime. He was one of the few people to retain his post following the 2004 presidential election.
In this election, he is representing the United National Front, the country's largest opposition voting bloc, the BBC reported. Abdullah is expected to pose the biggest threat to Karzai partly because of his name recognition.
In the 1980s, he was an adviser to the Mujahidin leader Ahmed Shah Massoud, who was killed in 2001 and is considered a national hero, according to the Washington Post.
He has talked about fixing government corruption and changing the government to a parliamentary system, according to the Associated Press. In addition, he has expressed openness to negotiating with the Taliban.
Abdullah was born on Sept. 5, 1960 in the capital of Kabul to a Pashtun father and Tajik mother. He has tried to reach out to both groups by wearing their traditional garb.
Ashraf Ghani, a former Afghan finance minister and World Bank official, is considered a long-shot for the presidency, according to the Associated Press.
During his campaign, he has spoken of ridding the government of corruption, promoting women's rights, and establishing model economic zones in the country "by targeting provinces with the best potential for growth and increasing budget authority on the local level," he wrote in an Aug. 7 Wall Street Journal opinion piece.
He has sought campaign help from James Carville, who managed Bill Clinton's successful presidential bid in 1992. The two have modeled Ghani's campaign after President Barack Obama's 2008 run, calling his campaign "A New Beginning," reported the Washington Post.
In a 2003 NewsHour interview, he spoke of how Afghanistan was recovering from the war and said the country was subject to a dictatorship before the removal of the Taliban government.
"Moving from that to getting democratic government is the most important thing, I think, where credibility depends is whether you establish good governance, where rule of law established and where the population can have trust that corruption is not going to prevail, but a small elite is not going to benefit, while the majority of people are going to be deprived," he said.
Ghani, an ethnic Pashtun, was born in 1949 and grew up in Kabul. He studied at the American University of Beirut and Columbia University in New York City, where he received his master's degree and Ph.D. in anthropology.
Incumbent President Hamid Karzai was named interim Afghan leader in December 2001 after the U.S.-led removal of the Taliban regime for supporting the al-Qaida terrorist network. He was then elected president in 2004, but has recently found his popularity slipping due to reported corruption in the government.
Karzai briefly supported the Taliban in the 1990s, but broke with them amid signs they were falling under the influence of foreign Islamist extremists such as al-Qaida, reported the Associated Press. His father, a Pashtun tribal chief, was assassinated in 1999, purportedly by the Taliban.
In the current campaign, Karzai has said he wants to expand on his government's achievements on social and economic issues, such as infrastructure developments and the protection of women's rights, according to the BBC.
In general, he supports the presence of international troops in Afghanistan but has been a vocal critic of airstrikes that have killed civilians, in addition to insurgent fighters.
Karzai has allegedly been making deals with tribal leaders to secure the backing of the Pashtun population and reportedly promised cabinet posts and governorships to business and militia figures in exchange for their support, reported the Washington Post.
---- Compiled from wire reports and other media sources