South Carolina, Nevada primaries and Ohio special election: Nancy Mace, Sam Brown win

Tracking anti-abortion candidates again in tonight's primaries, I'm thinking about how some of these races will shape the issue this fall. In deep-red districts, Republican voters often choose from a slate of anti-abortion candidates. But many of their extreme positions are unpopular overall, and that could make a difference in competitive races. That may be why candidates that are less extreme on the issue are winning in primaries like Nevada's Senate race — Brown has championed a more moderate position, and his wife has opened up about an abortion she had when she was younger. Likewise, the anti-abortion candidate in Nevada's battleground 3rd District is far behind. The issue might not always rank at the top for voters in surveys, but the GOP seems willing to be a bit more moderate in races where an extreme anti-abortion candidate could turn voters off.

—Monica Potts, 538

As we've been documenting this primary cycle, the GOP is badly trailing Democrats when it comes to endorsing and nominating women in primaries, especially primaries where they can win in November. Tonight marked a milestone for the GOP, with Fedorchak — the projected winner in North Dakota's At-Large Congressional District — becoming the first non-incumbent Republican women to win an open primary for a safe red seat.

GOP women saw another, albeit smaller, victory with Biggs advancing to a runoff in South Carolina's 3rd. That said, her competitor, Burns, has Trump's endorsement, which doesn't bode well for her. All told, tonight's races will do little to add more women to the GOP conference.

—Meredith Conroy, 538 contributor

I'm still struck by what we saw go down in Ohio's 6th District tonight. A sleepy special in such heavily Republican territory — we're talking a very white, rural, blue collar district with vanishingly few college graduates — should not have that kind of result absent something larger going on underneath the surface. I'll be interested to see what Ohio guru Kyle Kondik writes in the coming days about the results we've seen, and as I mentioned earlier, I want to see if Democrats turn in another big overperformance in Colorado later this month. And not for nothing, but Biden's actually been polling decently in Ohio relative to his numbers elsewhere? So perhaps there's something to Scranton Joe's resilience in the Rust Belt. We'll see!

—Jacob Rubashkin, Inside Elections

My takeaway from tonight is that, once again, we saw some close shaves for incumbent members of Congress. Incumbents may be heartened by the fact that, so far, only one of them has lost renomination this cycle, and that was in an incumbent-versus-incumbent race caused by Alabama redistricting, so one of them had to lose. However, they shouldn't get too comfortable. Many incumbents have won renomination with pretty uninspiring vote shares in the 50s or 60s — Timmons is only the latest example. Therefore, I'm pretty confident it's only a matter of time until one of them loses. (In fact, I recommend tuning into our live blog on June 25 to see if Rep. Jamaal Bowman becomes one of them.)

—Nathaniel Rakich, 538