Long queues and malfunctioning machines marred the first hours of voting in some precincts across the US.
Some of the biggest problems on Tuesday were in Georgia, a state with a hotly contested gubernatorial election.
Voters reported waiting up to three hours to vote.
Voter Ontaria Woods said about two dozen people who had come to vote left because of the queues.
It’s Election Day. The polls are OPEN.
One vote could be the difference between winning and losing today – and the candidate whose supporters show up will be Georgia’s next governor.
It’s now or never. Let’s get it done. https://t.co/ibvTOolZIJ #gapol pic.twitter.com/f3XSO1Z9I2
— Stacey Abrams (@staceyabrams) November 6, 2018
At a poll site in Atlanta, voters waited in the rain in long lines that stretched around the building.
Hannah Ackermann said officials at the polling site offered various explanations for the delay, including blaming workers who did not show up and overloaded machines.
President Donald Trump and vice-president Mike Pence campaigned for Mr Kemp while former president Barack Obama and talk show host Oprah Winfrey were among those to join Ms Adams on the campaign trail.
I’m running for governor to ensure that our kids and grandkids grow up in safe communities with good schools and economic opportunity. This is a fight for our future and I humbly ask for your vote today -> https://t.co/HOkW7MRdmd #gapol #gagop #tcot #gafirst pic.twitter.com/VADtDYvLCb
— Brian Kemp (@BrianKempGA) November 6, 2018
The state has been strongly Republican in recent decades but is seen to now be a Democratic target.
TODAY IS ELECTION DAY. LET YOUR VOICE BE HEARD??VOTE!!
— Jimmy Carter Library (@CarterLibrary) November 6, 2018
Former president Jimmy Carter, who was governor of Georgia before his stint in the White House, has also backed Ms Abrams.