Speculation is rife on who will replace the Senate seat of Republican John McCain who died on Saturday at the age of 81 after contracting a brain tumour.
Shortlisted candidates include the senator’s late wife Cindy McCain, the chairwoman of a beer distribution company who made public appearances in place of her husband prior to his death.
Primaries decide the offices of elected officials at federal and state level, as well as local governors.
What time do polls shut in Arizona?
Polls in Arizona open at 5pm BST today (9am local time) and close at 6am BST tomorrow (10pm local time tonight).
In Arizona, voters will choose their party nominees for a seat in the Senate, nine in the House and a governor.
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The House has nine seats, five of which are held by Republicans and four by Democrats.
Republican Doug Ducey is the current state governor and is seeking a second term.
How can you vote?
Voters must be registered and must show proof of identity at polling stations.
This can include either one photo ID from a pre-approved list or two non-photo IDs with the name and address of the person voting.
Donald Trump has not endorsed any of the three Republican candidates in the Senate race to replace Mr McCain.
What time do polls close in Florida?
Polls opened in Florida at 12pm BST (7am local time) and close at midnight BST (7pm local time).
How can you vote?
Florida is a closed primary state meaning people can only vote if they are registered members of the party prior to election day.
Voters who registered can cast their vote in person at the polls today as the deadlines for postal votes and early votes have now passed.
People must bring a valid photo ID, which must be one of 12 acceptable forms.
The full list of accepted IDs can be found here.