The rivals are running almost neck-and-neck in national polls
US Presidential Election 2012
Tens of millions of Americans have begun voting to decide whether to re-elect President Barack Obama or hand the job to Republican Mitt Romney.
Polling stations have opened on the East Coast and in parts of the Midwest - a winner could be known by midnight.
The voting ends a hard-fought race that began nearly two years ago and has cost more than $2bn (£1.3bn).
Polls show the race is neck and neck, although the president holds a slender polling lead in crucial swing states.
National polls by Washington Post/ABC News and the Pew Research Centre both give Mr Obama a three-point edge over his rival.
Race to the White House
Obama
50%
Romney
47%
Poll of polls,4 November
As many as 30 million voters have already cast their ballots, with more than 30 states allowing either absentee voting or in-person early voting.
On the stroke of midnight, the first votes were cast and quickly counted in the tiny village of Dixville Notch in New Hampshire. They resulted in a tie with five votes each for Mr Obama and Mr Romney.
Polling stations will begin closing in eastern states at 19:00 EST (00:00 GMT).
Mr Obama has already voted in his adopted hometown of Chicago, becoming the first sitting presidential candidate ever to vote early. Mr Romney is expected to cast his own ballot in Belmont, Massachusetts, later on Tuesday.
The election is decided by the electoral college. Each state is given a number of electoral votes in rough proportion to its population. The candidate who wins 270 electoral votes - by prevailing in the mostly winner-take-all state contests - becomes president.
The president appeared at rallies with singer Bruce Springsteen and rapper Jay-Z. He acknowledged frustration with the still-lagging economy but told voters "our work is not done yet".
"We've come too far to turn back now," the president said in Ohio. "We've come too far to let our hearts grow faint... We'll finish what we started. We'll renew those ties that bind us together and reaffirm the spirit that makes the United States of America the greatest nation on Earth."