Here are three trends from those primaries that can help us better understand the mood of the Republican and Democratic base going into a midterm election when majorities in both chambers of Congress could be up for grabs.
1. Are Republican voters going to remember — or repeat — Alabama?
Roy Moore was Republicans' worst nightmare. Primary voters nominated a seriously flawed candidate for the special election for the Senate in Alabama in 2017, and the party ended up losing a general election that, on paper, it should have won.
It could be on the verge of happening again, this time in West Virginia.
GOP Senate candidate Don Blankenship is a former coal baron who served a year in jail for violating mine safety regulations after a deadly explosion at one of his company's mines. He's launched a racially charged campaign against Senate Majority Leader Mitch McConnell (R-Ky.), which has intensified GOP efforts to tank Blankenship before they fear he tanks them.
Yet primary polls suggest that Blankenship could still beat two experienced Republican politicians, Rep. Evan Jenkins and state Attorney General Patrick Morrisey.
A Blankenship win could be disastrous for Republicans as they try to unseat Sen. Joe Manchin III (D-W.Va.) in one of the most pro-Trump states in the nation. Trump won the state by more than 40 points, and not even he thinks Blankenship is strong enough to beat Manchin in November.
2. Do messy GOP primaries give an opening to (wealthy) outsiders?
A big reason Blankenship is around at all is that he's been able to contrast the bickering between the other two politicians with his political novelty, which is helpful, given that outsiders are very on-trend in politics.
It's a play that businessman and former state representative Mike Braun is employing with some success in Indiana's GOP Senate primary. There, two members of Congress have been locked in an ugly primary fight for the right to run against Sen. Joe Donnelly (D-Ind.), another vulnerable Senate Democrat.
As GOP Reps. Todd Rokita and Luke Messer duke it out, Braun has surged in the polls by throwing some $6 million into TV ads, more than the two congressmen have spent combined.
A Braun win isn't nearly as catastrophic for the GOP in Indiana as Blankenship would be in West Virginia — Washington Republicans say all three GOP candidates in Indiana have a chance against Donnelly. But it would be notable if two relative outsiders beat some of Republicans' top recruits of 2018.
There's a similar situation playing out in a special congressional election in Ohio. Ten Republicans are running for a seat in Ohio's 12th District that was vacated this year by Rep. Patrick J. Tiberi (R). The front-runners are state Sen. Troy Balderson (R) and, you guessed it, an outsider: Melanie Leneghan, a trustee for a suburb of Cincinnati. No matter who wins, Democrats think they have a chance to pick up this seat, which Trump won by 11 points, in the special election in August. (Democrats' confidence is coming from winning a Pennsylvania special election deep in Trump country in March.)
Less competitive congressional seats also haven't escaped primaries. In North Carolina, GOP incumbents Reps. Walter B. Jones and Robert Pittenger each face spirited challengers from candidates who haven't served in Congress.
3. Should Democrats be worried about their party's purity battle?
Democrats have their primary drama, too. In Ohio, they are hoping to make a rare serious run at the open governor's seat. (Ohio Gov. John Kasich, a Republican, is term-limited and considering a 2020 run against Trump.)
The front-runner is Richard Cordray, a former state attorney general and former head of the Consumer Financial Protection Bureau in Washington. But he was unable to lock up the primary. Dennis Kucinich, a colorful former congressman and well-known figure on the left, got in at the last minute with an endorsement from an outside group with ties to Sen. Bernie Sanders (I-Vt.). Observers say they'd be surprised if Kucinich beats Cordray, but they'll also be watching just how well Kucinich does with Ohio's more liberal voters. If he does well, it could spell trouble for Democrats in November in this race.
That's a much bigger problem than one governor's mansion. As The Washington Post's Dan Balz writes, winning governor's races is key for Democrats' plan to eat away at Republican dominance in the states before it's too late; Democratic governors can veto partisan electoral maps that Republican state legislatures draw setting state and congressional districts for the next decade.