Who won and who lost in Tuesday’s primary elections.

Voters in a handful of states weighed in on key contests in Tuesday’s primaries. Here is a rundown of some of the most notable wins and losses.

New York

• Gov. Kathy Hochul won her Democratic primary, defeating Jumaane Williams, the New York City public advocate, and Representative Tom Suozzi of Long Island.

• Ms. Hochul will face Representative Lee Zeldin of Long Island, who won the Republican primary. He defeated three rivals, including Andrew Giuliani, a former Trump White House aide and the son of Rudolph W. Giuliani, the former New York City mayor and Trump lawyer.

• Ms. Hochul’s running mate, Lt. Gov. Antonio Delgado, whom she appointed to the position in May, won his Democratic primary, defeating Ana María Archila, the running mate of Mr. Williams, and Diana Reyna, the running mate of Mr. Suozzi.

Illinois

• Darren Bailey, a far-right state senator who was endorsed on Saturday by former President Donald J. Trump, won the Republican nomination for governor. He will face the Democratic incumbent, Gov. J.B. Pritzker.

• Representative Sean Casten, a moderate Democrat, defeated a progressive House colleague, Representative Marie Newman, in a primary for the newly drawn Sixth Congressional District.

• Representative Mary Miller, a 2020 election denier who has spoken admiringly of Adolf Hitler, won her Republican primary against fellow Representative Rodney Davis.

Oklahoma

• Representative Markwayne Mullin advanced to a runoff with T.W. Shannon, a former speaker of the Oklahoma House, in the Republican special primary for the Senate seat being vacated by James M. Inhofe, who is retiring. The winner of the special election in November will hold the seat until January 2027.

Colorado

• Joe O’Dea, a construction company owner who favors some access to abortion, won the Republican primary for Senate in Colorado, defeating a far-right challenger whom Democrats had tried to help because they thought he would be easier to beat in the general election.

• Pam Anderson, a longtime local election official in Jefferson County, won the Republican primary for secretary of state, defeating Tina Peters, a county clerk and election denier. Ms. Anderson will face the Democratic incumbent, Jena Griswold, who was unopposed in her party’s primary.

• Representative Lauren Boebert, one of Mr. Trump’s most ardent supporters, won the Republican nomination in the Third Congressional District.

• State Senator Barbara Kirkmeyer won the Republican nomination in the newly drawn Eighth Congressional District and will face Yadira Caraveo, a pediatrician and state lawmaker who was unopposed in the Democratic primary.

Mississippi

• Representative Michael Guest, who supported a Jan. 6 investigation but voted to overturn the 2020 election results, won the G.O.P. runoff in the Third Congressional District, defeating a pro-Trump challenger, Michael Cassidy.

• Mike Ezell, the sheriff of Jackson County, defeated Representative Steven Palazzo, a Republican facing an ethics investigation, in a primary runoff in the Fourth Congressional District.

Reid J. Epstein and Jennifer Medina contributed reporting.