Liberians are choosing a new president in a run-off vote between Vice-President Joseph Boakai and former international footballer George Weah.
Mr Weah, 51, won the first round, but did not secure the required 50% of the vote for an outright victory.
Legal challenges delayed the vote to replace Ellen Johnson Sirleaf, Africa’s first elected female president.
Liberia, which was founded by freed US slaves in the 19th Century, has not had a smooth transfer of power in 73 years.
More than two million people are eligible to cast their ballots in the nation of 4.6 million people. Polls will close at 18:00 local time (the same time GMT).
Who are the contenders?
The contest between Mr Boakai and former topflight footballer Mr Weah has been a stop-start exercise beset with legal wrangling, the BBC’s Umaru Fofana reports from the capital, Monrovia.
Mr Boakai, 73, has been Liberia’s vice-president for 12 years but does not seem to enjoy the support of his boss, our correspondent says.
“This is a great day because it is a test of democracy,” he said after casting his vote.
Mr Weah is hoping that it will be third time lucky.
The former AC Milan and Paris Saint-Germain player defeated Ms Johnson Sirleaf in the first round in 2005 but lost to her in the subsequent run-off.
In the following election’s run-off, in 2011, when he ran as a running mate to the opposition candidate, his coalition boycotted the vote, citing irregularities.
Why was the vote delayed?
A representative for the opposition Liberty Party, Charles Brumskine, who came third in October’s first round, challenged the result, saying it had been marred by “massive fraud and irregularities”.
But earlier this month the Supreme Court ruled that evidence of fraud was insufficient to merit a re-run of the opening round, and the run-off, originally due on 7 November, was announced.
Why the day after Christmas?
By law the elections must be held on a Tuesday and before the end of December, our correspondent writes.
The day after Christmas ended up being the only available date after another legal challenge, this time by the vice-president.
Mr Boakai insisted that the voters’ roll had not been cleaned up as ordered by the Supreme Court.
That ruling was only handed down last Thursday, so some in this Christian-majority country have put festivities on hold until after the polls.
“Those celebrations will happen on 29 December,” said one university student.
Will the vote be fair?
Weah supporters alleged some ballot-rigging, although there was no immediate official confirmation. George Weah himself said, after casting his vote, the election had been “peaceful and good”.
Goodluck Jonathan, the former Nigerian president, who is an observer at the election, told the BBC he was certain it would be free and fair despite “some challenges”.
Ms Johnson Sirleaf praised a violence-free electoral process, saying “the ballot box has replaced bullets and electoral disputes are settled through the courts”.
Why is this election so important?
This will be the first time for many generations that Liberians witness a transfer of power from one elected leader to another.
Ms Sirleaf took office in 2006, after her predecessor, Charles Taylor, was forced out by rebels in 2003, ending a long civil war.
Taylor is currently serving a 50-year prison sentence in the UK for war crimes related to the conflict in neighbouring Sierra Leone.
The result of the election is expected later this week.