Both Mr Trump and his Democratic challenger Joe Biden are running neck and neck in a number of swing states.
The president is projected to have held the must-win state of Florida - a major boost to his re-election bid.
But Mr Biden could snatch Arizona, a once reliably conservative state. The vote caps a long and bitter race.
Other key states such as Georgia, Pennsylvania, Wisconsin, Michigan and North Carolina are toss-ups.
With the nation on edge, the final result may not be known for days as postal votes are tallied.
More than 100 million people cast their ballots in early voting before election day on Tuesday - setting US on course for its highest turnout in a century.
Control of Congress is also at stake. As well as the White House, Republicans are vying to hang on to a Senate majority.
Republicans have lost a Senate seat in Colorado, but gained one in Alabama.
Mitch McConnell, the Republican Senate leader, and Trump ally Lindsey Graham have both been re-elected.
The House of Representatives is expected to stay in Democratic hands.