Turnout, expected to be 50-60 percent, could be crucial. Pollsters say lower participation could favour Renzi, as hostility to his reform is strongest among young voters and those in the poor south, segments of the population that often don't bother to vote. The referendum does not require a quorum to be valid.
A turnout above 60 percent could also make the result more unpredictable as it would suggest many voters who said they planned to abstain ended up going to the polls.
"It's very hard to decide," said 36-year-old Luca Di Giovanni, who runs a newsstand in Rome. "Yes is a vote for change, which should be good, but the issues are complicated and I'm not sure that I trust Renzi."
With bookmakers' odds suggesting a roughly 75 percent chance of a win for 'No', speculation is rife about what Renzi will do in the event of defeat.
He is widely expected to resign and has said he will play no role in any unelected "technical" government President Sergio Mattarella may try to put in place. Some of his allies have urged him to stay in power regardless of the result.
"I voted 'Yes'. I have really had enough of these continuous changes of government. Renzi isn't the best but all the others aren't any better ... but probably 'No' is going to win," said Giorgio Valentini, after voting in Rome early in the morning.
The result of exit polls will be announced as soon as voting ends and the count begins at 11 p.m. (2200 GMT). After around 30 minutes, the first projections of the result will be announced on the basis of actual votes counted.
If the result is not close, the winner could be clear after the second projection, some time between midnight and 1 a.m. In a very close race, the winner may not be known until the count is completed, probably between 2 and 3 a.m.
Economy Minister Pier Carlo Padoan sought to calm nervous markets on Friday, saying there was "no risk of a financial earthquake" if 'No' wins, though there may be "48 hours of turbulence".
Market jitters have concentrated on Italy's banks, saddled with 360 billion euros ($380 billion) of bad loans, and most specifically on Monte Dei Paschi di Siena, its oldest and third largest lender.
The bank needs to raise 5 billion euros ($5.3 billion) by the end of the year to plug a capital shortfall or risk being wound down. Government officials say potential investors may be deterred by political instability if 'No' should win.