Trump leads the Republican field in the country's first primary, while Florida Senator Marco Rubio tries to establish himself as the chief rival to Trump and Texas Senator Ted Cruz.
In the two-person race for the Democratic nomination, Vermont Senator Sanders has an advantage over Hillary Clinton in New Hampshire after his narrow second-place finish in Iowa last week.
He must win to have a chance of staying competitive with the former secretary of state and first lady as the race moves to more diverse states.
The New Hampshire primary gives momentum to the winners heading into the next contests in South Carolina and Nevada as candidates race to pick up delegates for their parties' nominating conventions. Those who fare poorly could see donations dry up and face pressure to withdraw from the race.
While critics also argue that New Hampshire is too small and too white to play such a major role in picking presidents, its defenders say the country is well-served because the primary requires close contact with voters, not just name-recognition or advertising cash.
The first ballots were cast early today in the tiny town of Dixville. Sanders won over all four Democratic voters in the town, while Ohio Governor John Kasich sneaked past Trump, 3-2, among Republicans.
State law requires polls to be open between 11 am and 7 pm today. About 20 remain open until 8 pm.
The enthusiasm behind Trump, a real estate mogul who has never held political office or run in an election, and Sanders, an avowed democratic socialist, underscore the public's impatience with the current political system.
