See also Tunisia Video: What Happens If No One Votes? The Return of Ben Ali....
UPDATE 1645 GMT: The head of the electoral commission, Kamel Jendoubi, has announced that the turnout is approaching 70% and is near 80% in some districts. He said results would be declared on Tuesday.
UPDATE 1015 GMT: Two videos from today's voting --- Al Jazeera English correspondent Nazenine Moshiri outlines the system and talks to a voter:
Rached Ghannouchi, the leader of the al-Nahda Party, is told to get in the queue for voting after he apparently tried to cut into the line. Some in the crowd shout "Degage (Get out)!", the chant used against former President Ben Ali during the January uprising:
UPDATE 0810 GMT:Was this the first vote in Tunisia's first democratic election in decades? A woman casts her ballot in advance voting in the Tunisian Embassy in Australia
Al Jazeera English summarises:
Nine months after a popular uprising that ended decades of authoritarian rule, Tunisians have begun to vote for new leaders who will write the rules of the country's new political system.
Polls opened at 07:00 local time (06:00 GMT) on Sunday, with about 4.4 million registered voters set to pick a 217-member constituent assembly. That multi-party body will, in addition to drafting a new constitution, also be charged with appointing an interim president and a caretaker government for the duration of the drafting process.
More than 11,000 candidates are running in the election, representing 80 political parties. Several thousand candidates are running as independents.
Polls close at 19:00 local time (18:00 GMT), and results will be declared on Monday.
The government says that 40,000 police and soldiers have been deployed to prevent any possible protests escalating into violence. Shopkeepers in Tunis, meanwhile, said that people had been stockpiling milk and bottled water in case any unrest disrupted the supply of necessities.
Kamel Jendoubi, the country's election chief, declared his independent ISIE polling commission "ready and confident" ahead of voting, while the European Union's observer mission said there was "almost no chance of cheating or falsifying results".
The mother of Mohamed Bouazizi, the young vegetable seller whose self-immolation last December set of the Tunisian revolt, said that the elections were a victory for dignity and freedom.
"Now I am happy that my son's death has given the chance to get beyond fear and injustice," Manoubia Bouazizi told the Reuters news agency. "I'm an optimist, I wish success for my country."
The election is the first for many Tunisians where they have had a range of parties to choose from.
"I am 39 years old and this is the first time I'm voting, so it's about time," Mehdi Barabdullah, a voter at a polling station in Tunis, told Al Jazeera.
"I'm very very happy for Tunisia. It's a historical time for us. This piece of paper that I can show you [marking my registration to vote] is a very important paper for us. I am voting for the future of my daughter and I'm absolutely thrilled by it."
Tunisia was the country that trigged what became known as the 'Arab Spring' after a month-long uprising forced then-President Zine El Abidine Ben Ali to flee to Saudi Arabia.
The protests quickly spread to neighbouring Egypt and Libya, along with countries in the Middle East such as Syria, Yemen and Bahrain.
The country has been relatively calm in the weeks leading up to the election, with the exception of isolated protests against Nessma TV. With no other genuine democracies in the Arab world, many across the region are paying close attention to Tunisia's democratic transition.
Sunday's election for the constituent assembly is a litmus test for the depth of change the country has seen since January; and nerves were high on the eve of the vote.
Tunisian authorities arrested at least two well-known activists on Saturday evening, both of whom have been prominent critics of the interim government led by Beji Caid Essebsi.
Bilal Dhaifallah, an independent Salafist who is against the elections and participated in protests in the Kasbah against the interim government, as well as against Nessma TV, was arrested briefly on Saturday evening.
Dhaifallah told Al Jazeera that police came to his house in Mejrine, a suburb to the east of Tunis, and held him for several hours, before releasing him.
They questioned him over his Facebook profile photo, which shows him in Libya holding a Kalashnikov assault rifle, he said.
"They searched my house looking for weapons and went through my computer, but they didn't find anything," he said, adding that the photo was just a souvenir and he had never brought weapons into Tunisia.