The New York Times

1. Steve Hilton Wins Second Spot in California Governor Race, Beating Tom Steyer

   Steve Hilton, a Republican endorsed by President Trump, will face Xavier Becerra, a Democrat, in the general election. Tom Steyer, another Democrat, will not advance.

2. Sanders-Backed Progressive Advances in California Swing District Against Valadao

   Randy Villegas will face the incumbent, David Valadao, a Republican who has survived numerous challenges in a competitive district.

3. Rep. Kevin Kiley, Independent, to Face Richard Pan in California House Race

   Mr. Kiley dropped his Republican affiliation earlier this year. The newly drawn Sixth Congressional District is widely considered to be favorable for Democrats.

4. Takeaways From Tuesday’s Primary Elections in Maine and South Carolina

   Graham Platner won the Democratic nomination for Senate and quickly turned his booming, populist message against Susan Collins, the Republican incumbent in perhaps the top battleground in the country.

5. Lindsey Graham Wins Republican Senate Primary in South Carolina

   Mr. Graham, a four-term incumbent, is the favorite to win the general election in a solidly Republican state.