Arizona is a coveted target for Democrats, who hope to flip House seats and the state legislature. Yet party leaders have repeatedly tried and failed to win big here. Hillary Clinton held out hope of carrying Arizona in 2016, but Donald Trump won by more than three percentage points. The state has elected deeply conservative leaders like former Gov. Jan Brewer, and it has been a testing ground for harsh immigration policies later embraced by Mr. Trump. Women are playing leading roles in both parties, with Republicans fielding strong female candidates at all levels — a reminder after Mrs. Clinton’s loss that women do not vote in a bloc.

The state embodies dynamics seen across the country. Shocked and despairing at Mr. Trump’s election, women on the left concluded they had been complacent and are now diving into politics, many for the first time. Democrats are hoping to capitalize on a growing Hispanic electorate; Republicans are testing whether their close embrace of the president helps or hurts.

Among the state’s marquee races is an all-out fight for the Senate seat being vacated by Jeff Flake, with candidates including Representative Martha McSally, the Air Force’s first female fighter pilot; Kelli Ward, a former state senator and hard-right politician known for her conspiracy theories; and Joe Arpaio, the sheriff whose anti-immigrant stances cost him his job in 2016 on the Republican side. Representative Kyrsten Sinema is running against another woman and several men on the Democratic side. On the state level, January Contreras, a Democrat, is the first Latina to run for state attorney general.

There’s also a #MeToo-inflected special election to replace Representative Trent Franks, who resigned under pressure in a sexual harassment scandal. On April 24, Debbie Lesko, a former state senator who beat 11 Republican male primary challengers as a full-throated Trump supporter, will face off against Hiral Tipirneni, a doctor and political newcomer who trained with Emerge America, one of several groups that recruit Democratic women to run for office.

Still, Arizona remains a state that has not had a Democratic senator since 1995 and where Republicans have the trifecta of governor and both houses of the legislature. Entrenched conservative values will clash this year with a liberal fervor that often plays out at the local level, in grinding, unglamorous work.