The people of Turkey are voting in a referendum on changing the constitution, which was drafted under military rule in the early 1980s.
The government says it wants to bring the constitution more in line with European Union standards.
Opponents argue that the governing party, which has its roots in political Islam, is seeking dangerous levels of control over the judiciary.
The referendum is expected to produce a close result.
The 26 amendments, many of them backed by the EU, are being presented to voters as improvements on the 1982 constitution, says the BBC's Jonathan Head in Istanbul.
But two are seen by the opposition as granting the government excessive influence over the judiciary.
The ruling Justice and Development Party (AKP), led by Recep Tayyip Erdogan, has argued the changes will strengthen Turkish democracy.
It is the sixth time in nearly half a century that Turkey is voting on a constitutional amendment, with the last referendum held in October 2001, Turkey's Anatolia news agency reports.
Polling stations will close at 1400 GMT and results are expected several hours later.
The secular opposition say that they will vote against the amendments.
They accuse the AKP of trying to seize control of the judiciary as part of a back-door Islamist coup.
Buke Acar, a voter in the capital Ankara, said she was voting "No" in order defend the rule of law.
"Not securing the independence of the judiciary is a big threat in democratic countries," she said.
The opposition may be joined by critics protesting at the speed with which the reforms have been pushed through.
The present constitution was introduced in 1982.
"The constitution changed with the junta in the military coup days," voter Mehmet Yildirimlar told the Associated Press news agency in Diyarbakir.
"We stood against them in those days, because a military coup is no good.
"That's why we are here today. We voted 'Yes' for the sake of our children and youth. Because we have suffered a lot."
Mr Erdogan has been travelling around Turkey for the past three weeks, trying to drum up support for his reforms.
The AKP has clashed repeatedly with Turkey's highest courts, which see themselves as guardians of the country's secular values.
In 2008, the AKP narrowly avoided being outlawed by the Constitutional Court for allegedly undermining Turkey's secular system.
But Mr Erdogan told the BBC last week his party had never discriminated between secular or non-secular Turks.
He said he believed that secularism should apply to the state, not the people.