As well as the White House, Democrats and Republicans are locked in a tight race for control of the US Senate.
Republicans hold a 53-47 majority in the upper chamber of Congress, meaning the Democrats are seeking a net gain of four seats.
Five seats, including some tight battleground contests in Georgia and North Carolina, are yet to be decided.
Democrats are also fighting to maintain their majority in the lower chamber, the House, and are ahead in the polls.
But with many votes still to be counted, the final result of both races may not be known for some time.
This year’s congressional election is running alongside the battle for the White House between Donald Trump and his Democratic challenger Joe Biden.
A Democrat-controlled House and Senate would have the power to obstruct the plans of a second-term President Trump, or push through the agenda of a first-term President Biden.
Of the 35 Senate seats up for grabs, 23 are Republican-held and 12 are Democrat.
Senators serve six-year terms, and every two years a third of the seats are up for re-election.
Who are the winners and losers?
By early on Wednesday, Democrats had managed a net gain of one seat in the Senate election. This means three seats would have to flip to their control for the party to guarantee control of the chamber for the first time in six years.
Democratic former governor John Hickenlooper won a key Colorado seat from the Republican incumbent Cory Gardner.
Mr Hickenlooper, who stood for the Democratic nomination for president, was governor of Colorado for two terms from 2011 until last year. His rival was considered particularly vulnerable because of his allegiance to President Trump.
In Arizona, former astronaut Mark Kelly defeated Republican incumbent and former fighter pilot Martha McSally. He earlier said he was “confident that when the votes are counted, we’re going to be successful in this mission”.
However, Republican Senate Majority Leader Mitch McConnell and Trump ally Lindsey Graham have both been re-elected in their seats of Kentucky and South Carolina respectively.
And in Alabama, Republican candidate Tommy Tuberville took a seat from the Democratic incumbent Doug Jones.
Among the candidates for Senate this year were a pastor, a trucker and a football coach.
The results have already proved historic – with Democrats Ritchie Torres and Mondaire Jones, both in New York, becoming the first gay black members of Congress after they were elected to the House of Representatives.
Democrats Alexandria Ocasio-Cortez, Ayanna Pressley, Rashida Tlaib and Ilhan Omar secured re-election to the House. Together they have been dubbed ‘The Squad’.
In Oklahoma, the state’s sole Democratic member of the House, Kendra Horn, has conceded to her Republican challenger Stephanie Bice.
One Republican candidate who has won a seat in Congress has previously promoted the far-right QAnon conspiracy theory. Marjorie Taylor Greene, of Georgia, was hailed as a “future Republican star” by President Trump earlier this year.
Voters are also choosing representatives in their local state senates – and in Delaware, Democratic candidate, Sarah McBride has made history as the country’s first ever trans state senator.
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