People in Scotland are voting on whether the country should stay in the UK or become an independent nation.
Voters are answering "Yes" or "No" to the referendum question: "Should Scotland be an independent country?"
With 4,285,323 people - 97% of the electorate - registered to vote, it is expected to be the busiest day in Scottish electoral history.
Votes will be cast at 5,579 polling stations until 22:00 on Thursday. The result is expected on Friday morning.
Strict rules mean the BBC - in common with other broadcasters - is not allowed to report details of campaigning until after the polls close.
With an hour to go until the polls close, the Electoral Commission said: "Polling stations are busy, but we've not heard of any long queues.
"If you're at the polling station by 10pm and you're in a queue, you will get to vote."
During the day, a number of councils around the country said polling stations were busy, with some seeing queues both ahead of the polls opening and throughout the morning.
Stirling Council area counting officer Bob Jack said: "There has been a steady stream of voters and we have been very busy."
In East Renfrewshire, there were queues before the polls opened this morning and a steady stream since, a council spokeswoman said. Some voters had been kissing their ballots, she added.
At the scene
By BBC Scotland correspondent James Cook
It was a grey dawn in Edinburgh, the moisture clinging to the old buildings, seeping into the sandstone.
At Tollcross Primary School, the weather didn't seem to deter the voters. The first arrived at five minutes to seven, before the polls had opened, clutching her voting card, eager to be the first to place her cross.
As the morning wore on and the darkness began to recede, the first trickle of voters became a stream.
A paramedic in his hi-vis jacket, a businessman in a smart suit, schoolteachers, a man clutching his baby to his chest; all were heading to the same destination - the ballot box for a private moment with a pencil and paper - and a choice: Yes or No.
These were personal moments, private and privileged, there was a stillness about the scene.
The airwaves, full of chatter for so long, had fallen silent as required by law. This was the moment, not for politicians or commentators, but for Scotland to speak. Tomorrow, we will find out what it said.
Police Scotland have confirmed a 67-year-old woman was arrested and charged in connection with an alleged assault on a female following an incident at Shettleston Community Centre, a polling place in Amulree Street, Glasgow, at around 13:00 BST.
The woman is believed to come from Merseyside. A report will be submitted to the Procurator Fiscal.
Earlier, a man was arrested outside a polling station in Clydebank after an alleged assault. Police Scotland said the man was detained on Faifley Road at 08:30.
Once the polls have closed, ballot papers will be counted in each of Scotland's 32 local authority areas.
These will include votes cast from the 789,024 postal vote applications, which was the largest volume of registration for postal votes ever in Scotland.
After votes have been tallied, the counting officer in each area will communicate the result to the chief counting officer Mary Pitcaithly in Edinburgh.
With her approval they will then make a declaration of the result.
Once the results from all 32 local authority areas are known, Ms Pitcaithly will declare the result of the referendum at the Royal Highland Centre outside Edinburgh.
Ms Pitcaithly has said she will announce the result at "breakfast time" on Friday.
The result is most likely to be between 06:30 and 07:30, according to Elections Scotland.
That is because the final Scottish declarations in the 2010 UK parliamentary elections and the 2011 Scottish parliamentary elections declaration were made at those times respectively.
However, running totals - which can be made from the first declaration onwards - may indicate a result earlier in the morning.
The bulk of local results are expected to come in between 03:00 and 06:00.
Because the polling stations are expected to be so busy, counting officers have put measures in place to reduce the risk of queuing.
The remote nature of some Scottish regions also means bad weather could delay the receipt of ballot boxes at counting centres, in turn delaying the national result.
The Western Isles declaration may be delayed after Stornoway airport closed owing to fog, meaning some ballot boxes from other islands might have to be taken there by boat and by road.
Helicopters and boats are being used to transport ballot boxes to counts in areas such as Argyll and Bute.
There was concern on social media that some rail passengers may be delayed in getting to the polling stations after an incident caused disruption on the line near Dunkeld.
Network Rail said the windscreen of an East Coast train from London Kings Cross to Inverness was struck by an object in a tunnel. No-one was thought to have been injured.
Elections Scotland said recounts would only be allowed at a local level on the basis of concerns about process, not the closeness of a result.
You can also watch and listen to all the live television and radio coverage on the BBC News website.
How the BBC reports polling day
Strict rules mean the BBC, like other broadcasters, isn't allowed to report details of campaigning while the polls are open.
In all national elections, the BBC is legally required both by its own charter and electoral law to adopt a code of practice.
The BBC Trust adopts an equivalent approach for national referendums and publishes Guidelines for all BBC output to supplement its normal editorial guidelines in the very specific circumstances of an election or referendum period.