A high turnout has been predicted, but the outcome may not be known for several days if the results are as close as polls have indicated.
Whoever wins the White House may have their hands tied by Congress, which is also up for grabs in Tuesday’s vote.
Democrats have a slim majority in the Senate, while Republicans narrowly control the House of Representatives.
Republicans took a step towards winning control of the Senate on Tuesday night by wresting a seat in West Virginia from the Democrats.
But neither party seemed to have an advantage in the House.
Polls have closed in Georgia, North Carolina and Pennsylvania - three of the seven swing states expected to determine the outcome. The others are Arizona, Michigan, Nevada and Wisconsin.
Georgia Secretary of State Brad Raffensperger said that by new state law, early votes in the Peach State are required to be publicly reported one hour after polls close.
"You'll get a lot of results really quick," he said.