The primaries in Arizona and Florida on Tuesday will largely conclude a Republican nominating season dominated by President Trump, while also offering revealing insights into the direction of a Democratic Party wrestling with the way forward.

The Times will have live results starting at 7 p.m., when polls close in Florida.

Here are the most interesting races to watch:

Race to replace a Trump critic

The most high-profile race of the day may be the Republican Senate primary in Arizona, which illustrates how central Mr. Trump has become in Republican politics (and comes only three days after Arizona’s senior senator, John McCain, died of brain cancer). The race to replace Senator Jeff Flake, a Republican and an outspoken Trump critic who is retiring after a single term, has become a competition to see who can cling most tightly to Mr. Trump and his brand of hard-line conservatism.

The best-known figure in the three-way contest is Joe Arpaio, the former Maricopa County sheriff whom Mr. Trump pardoned last year, though he has been trailing in the polls. Mr. Arpaio’s presence in the race, however, has made it difficult on another hard-liner, Kelli Ward, to consolidate support from the most conservative Arizona voters.