Voters from both parties will select party nominees for both of the state's U.S. Senate seats.
Republican Lindsey Graham is running for a third term and faces six GOP challengers who say he's not conservative enough.
Voters will also select nominees U.S. Sen. Tim Scott's seat. He's running for the rest of the unexpired term of Jim DeMint. Scott was appointed by Gov. Nikki Haley to the Senate when DeMint resigned at the end of 2012.
Among other offices, voters will choose from a bevy of candidates who want to become state's superintendent of education and lieutenant governor.
In addition, five congressional primaries will be decided Tuesday.