Polling stations are open between 07:00 BST and 22:00 BST.
An estimated 46,499,537 people are entitled to take part in the vote - a record number for a UK poll.
It is only the third nationwide referendum in UK history and comes after a four-month battle for votes between the Leave and Remain campaigns.
In common with other broadcasters, the BBC is limited in what it can report while polls are open but you can follow the results as they come in across the BBC after polls close on Thursday evening.
The referendum ballot paper asks the following question: "Should the United Kingdom remain a member of the European Union or leave the European Union?"
Whichever side gets more than half of all votes cast is considered to have won.
The weather forecast for polling day is mixed, with thundery showers in the south-east of England, which could dry up later in the day.
Sunshine and heavy showers are forecast for Northern Ireland and Scotland but it is set to be drier and brighter elsewhere.
After the referendum polls close at 22:00 BST, sealed ballot boxes will be collected and transported to the count venue for each of the 382 local counting areas.
These represent all 380 local government areas in England, Scotland and Wales, plus one each for Northern Ireland and Gibraltar.
Individual areas' results will then be declared throughout the night, along with results from 11 regional counts.
Depending on how close the poll is, the result may become clear before the final national result is officially declared by the Chief Counting Officer, who will be based at Manchester Town Hall.
The Electoral Commission estimates a final result "around breakfast time" on Friday.