From California House races to women winning big, 9 things to know about Tuesday's primaries

From women hoping to make history to a recall vote for a California judge who issued a controversial sentence to a college student convicted of sexual assault, June 5 was a busy night of primary elections nationwide.

Primaries were held in eight states: Alabama, California, Iowa, Mississippi, Montana, New Jersey, New Mexico and South Dakota.

President Trump took to Twitter Wednesday morning to praise Republicans and John Cox, the GOP gubernatorial candidate in California who secured enough votes to make it to the general election in November.

“Great night for Republicans! Congratulations to John Cox on a really big number in California. He can win,” Trump said. “So much for the big Blue Wave, it may be a big Red Wave. Working hard!”

Read on for a look at nine primary moments you should know about.

Newsom, Cox advance to California gubernatorial race

Republican John Cox, who has the support of President Trump, will appear on the ballot against Democrat Lt. Gov. Gavin Newsom later this year.

Cox received about a quarter of the votes counted so far, easily outpacing former Los Angeles Mayor Antonio Villaraigosa for the second-place finish. Newsom came in first by a comfortable margin.

Cox, 62, earned his wealth as a lawyer, accountant and investor in the Chicago area. He also owns thousands of apartments in the Midwest. Newsom, 50, is the former mayor of San Francisco.

Trump encouraged California voters to support Cox in the primary with multiple tweets, calling the businessman a “really good and highly competent man.”

On the morning of the primary, Trump said Cox “will make a BIG difference” in California, which he called a “high tax, high crime” state.

Congresswoman who opposed Trump forced into runoff

Martha Roby 2 Facebook

Republican Rep. Martha Roby, who criticized rescinded her endorsement of President Trump in 2016, failed to secure enough votes in Alabama's primary to avoid a runoff next month.  (U.S. House of Representatives)

Rep. Martha Roby, R-Ala., retracted her endorsement of Trump -- before he was elected president -- after an “Access Hollywood” tape of Trump saying vulgar things about women was published.

Nearly two years later, her seat is in danger. Roby failed to reach the 50 percent threshold in Alabama’s primary and will face Bobby Bright in a July 17 runoff. Bright is the former mayor of Montgomery, Ala., and only recently switched his party affiliation from Democrat. He used to represent the district in Congress until Roby defeated him in 2010.

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Roby, 41, has represented Alabama’s 2nd congressional district since 2011.

“Donald Trump’s behavior makes him unacceptable as a candidate for president, and I won’t vote for him,” Roby said at the time, adding, “Hillary Clinton must not be president, but, with Trump leading the ticket, she will be.”

Her lack of support for Trump has made her a target in the midterm elections. Bright even released a campaign ad in which he accused her of having turned “her back on President Trump when he needed her the most.”

Democrat Tabitha Isner won the Democratic primary and will face either Bright or Roby in the general election.

Women vying for governor win big

FILE - In this Dec. 5, 2017 file photo, Rep. Kristi Noem, R-S.D., and South Dakota gubernatorial candidate, speaks on Capitol Hill in Washington. Noem and state Attorney General Marty Jackley are competing for the Republican nomination for governor, the highest-profile and likely most expensive contest on the June 5, 2018, primary ballot. The winner is a favorite in heavily Republican South Dakota to take the governor's office in the November general election. (AP Photo/J. Scott Applewhite, File)

Rep. Kristi Noem won the Republican primary for Iowa governor.  (AP Photo/J. Scott Applewhite)

Several women secured their party’s nomination for governor in the primaries.

Rep. Kristi Noem defeated Attorney General Marty Jackley to become the Republican nominee for South Dakota’s gubernatorial race. She is the only woman South Dakota Republicans have nominated for the state’s top job. Noem, 46, is expected to face Billie Sutton, a well-funded Democrat and former professional rodeo cowboy who ran unopposed, in the general election.

In New Mexico, Democrats elected Rep. Michelle Lujan Grisham, 58, as the party’s nominee for governor. She will face Rep. Steve Pearce, a Republican, in the general election to replace term-limited Gov. Susana Martinez.

Democrats already control much of New Mexico politics, including the legislature and other statewide offices. A win for Lujan Grisham, who leads the Congressional Hispanic Caucus and has been an ardent critic of Trump, could shut out Republicans from redistricting efforts in 2021.

Incumbent Gov. Kay Ivey, a 73-year-old Republican, won the GOP primary in Alabama. She will face off against Walt Maddox, a Democrat, in the general.

“I’m grateful to the people of Alabama for their support throughout this journey, and I am honored to be chosen as the Republican nominee for Governor,” Ivey, who became Alabama’s second female governor in 2017 after Robert Bentley resigned, said in a statement to WBRC-TV. “I humbly ask for the people’s continued support, prayers and votes in November. Let’s keep up the good fight!”

In Iowa, Gov. Kim Reynolds is set to advance to the general election, as she ran unopposed. The 58-year-old will face Democrat Fred Hubbell, a wealthy businessman, in November.

Reynolds, a former lieutenant governor, took over as leader of the Hawkeye State after Terry Branstad became U.S. ambassador to China in 2017.

New Mexico poised to elect first Native American congresswoman

Deb Haaland poses for a portrait in a Nob Hill Neighborhood in Albuquerque, N.M., Tuesday, June 5, 2018. New Mexico voters will narrow the field in two competitive congressional races, including one in a district along the Mexico border involving a GOP-held seat that Democrats have long targeted. Haaland, a tribal member of Laguna Pueblo, is aiming to become the first Native American woman in Congress. (AP Photo/Juan Labreche)

Deb Haaland, a tribal member of Laguna Pueblo, is aiming to become the first Native American woman in Congress.  (AP Photo/Juan Labreche)

Democrat Deb Haaland won her party’s primary in New Mexico Tuesday night -- putting her closer to making U.S. history as the first Native American congresswoman. If she wins the general, she would represent New Mexico’s 1st congressional district, which encompasses Albuquerque.

Haaland is a former leader of the Democratic Party in New Mexico and a tribal member of the Laguna Pueblo.

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“Donald Trump and the billionaire class should consider this victory a warning shot: the blue wave is coming,” Haaland said after winning her primary.

Haaland will face Republican Janice Arnold-Jones in November’s general election for the seat vacated by Lujan Grisham. Arnold-Jones ran unopposed.

No party suffered mass casualties in California House races

Both Republicans and Democrats in California appeared to escape the state’s jungle primary relatively unscathed, as neither party was shut out of certain competitive House races. The jungle primary system pushes the top two finishers of a race to the November elections, regardless of party.

For Democrats, certain close House races are critical for taking back control of Congress in the 2018 midterm elections. At least two of their best pickup opportunities in southern California have yet to be officially decided, but Democrats avoided being shut out from the ballot in the vast majority of the state’s top battleground races.

Republicans led the pack by a wide margin in many key races Tuesday.

In the 48th congressional district, incumbent GOP Rep. Dana Rohrabacher was comfortably in first place with about 30 percent of the vote, despite being attacked by opponents for his ties to Russia. And in the 39th district, to replace retiring Rep. Ed Royce, Republican Young Kim was ahead with about 22 percent of the vote -- with Democrat Gil Cisneros less than 3 points behind.

Republican Diane Harkey advanced to the November election in the 49th congressional district with 25 percent of the vote as of Wednesday morning, leading the pack by about 8 points in the the race to replace outgoing GOP Rep. Darrell Issa.

Democrats need to pick up 23 GOP-controlled seats in order to take the House in the midterms. Out of California’s 53 House seats, Republicans hold 14, and seven of those districts backed Democrat Hillary Clinton in the 2016 presidential election.

Judge who sentenced Stanford swimmer recalled

FILE - In this May 15, 2018 file photo, Judge Aaron Persky poses for photos in Los Altos Hills, Calif. Persky says he would handle the sexual assault case of former Stanford University swimmer Brock Turner the same way today as he did almost exactly two years ago, even though it's the reason why he is the target of a June 5 recall election in Santa Clara County. Persky sentenced Turner to six months in jail. (AP Photo/Jeff Chiu, File)

Judge Aaron Persky, who sentenced Brock Turner to six months in jail after he was convicted of sex crimes, was recalled by voters in California. He is the first judge to be recalled in more than 80 years.  (AP Photo/Jeff Chiu)

The judge who sentenced a former Stanford University swimmer to six months in prison for sexually assaulting an unconscious woman was recalled by voters Tuesday.

Judge Aaron Persky sentenced Brock Turner, who was convicted of two counts of digitally penetrating an unconscious person and one count of assault with intent to rape, to six months in jail, but Turner was released from prison after only serving half that time. He was caught in January 2015 assaulting a woman behind a dumpster.

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The prison sentence set off a nationwide conversation about campus sexual assault and whether the nation’s judicial system takes the crime seriously enough -- even before the height of the #MeToo movement. Michele Dauber, a Stanford University law professor and friend of victim, launched a campaign to recall Persky.

“This is a historical moment in time. Women are standing up for their rights, and there is a national reckoning.”

- Michele Dauber, Stanford University law professor

The recall vote was considered to be one of the first electoral tests of the #MeToo movement’s political strengths.

Persky is the first California judge to be recalled in more than 80 years.

“The broader message of this victory is that violence against women is now a voting issue,” Dauber said in a statement. “This is a historical moment in time. Women are standing up for their rights, and there is a national reckoning.”

Assistant District Attorney Cindy Hendrickson will finish out the remaining four years of Persky’s term, the San Francisco Chronicle reported.

Rosendale will face Tester for Minnesota Senate

In this June 5, 2018 photo, Matt Rosendale addresses supporters in Helena, Mont., after winning the Republican nomination for the U.S. Senate. Rosendale will challenge Democratic incumbent Jon Tester in November. (Thom Bridge/Independent Record via AP)

Montana state auditor Matt Rosendale won the GOP nomination for U.S. Senate. He will face endangered incumbent Sen. Jon Tester, a Democrat, in the fall.  (Thom Bridge/Independent Record via AP)

Montana state auditor Matt Rosendale beat out the three other GOP contenders to secure his party’s nomination to face incumbent Sen. Jon Tester, an endangered Democrat, in the fall.

Rosendale, the 57-year-old former majority leader in the state Senate, was elected as Montana’s state auditor in 2016. He had the endorsements of Sens. Rand Paul, Mike Lee and Ted Cruz in the primary.

Tester, a more conservative Democrat, drew the ire of Trump earlier this year during the kerfuffle over the president’s pick to lead the Veterans Affairs Department. Adm. Ronny Jackson, who was the president’s physician, withdrew his name from consideration for the Cabinet post following allegations about his prescription-drug practices and use of alcohol. Jackson was also accused of wrecking a government vehicle while intoxicated.

The allegations were collected by Tester’s office, as he is the top Democrat on the Senate Veterans’ Affairs Committee.

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“I’ll fight for more freedom and prosperity for all Montana,” Rosendale said after his primary victory. “We need to send Trump some conservative reinforcing that will end the liberal constriction.”

Rosendale beat out three other contenders to win Tuesday’s primary: combat veteran Troy Downing, Judge Russ Fagg and state Sen. Albert Olszewski.

Menendez survives primary to face pharmaceutical executive

New Jersey senator Bob Menendez attends a ribbon cutting ceremony at Essex County Donald M. Payne, Sr. School of Technology in Newark, N.J., Monday, June 4, 2018. With the opportunity for at least two pickups, Democrats' road to controlling any part of Congress could cut through New Jersey this fall — but first primary voters will have their say. Incumbents face challenges in the Senate contest, where Democrat Menendez will face a well-funded former pharmaceutical executive, if both survive the primary. (AP Photo/Seth Wenig)

New Jersey Sen. Bob Menendez will face pharmaceutical executive Bob Hugin, a Republican, in the general election.  (AP Photo/Seth Wenig)

New Jersey Sen. Bob Menendez survived the Democratic primary after being ensnared in a corruption and bribery case last year. The trial ended in a mistrial after the jury said it could not reach a decision, but Menendez was “severely” admonished by the Senate Ethics Committee.

Menendez defeated publisher Lisa McCormick in the primary and will face pharmaceutical executive Bob Hugin, a Republican, in the fall.

Throughout the primary -- even though the two men are not appearing on a ballot together until November -- Hugin and Menendez did not miss any opportunity to take jabs at one another. Both candidates raked in millions of dollars in campaign contributions.

“My opponent, greedy drug company CEO Bob Hugin, is going to have to answer for his record of driving up prices for cancer patients while making millions for himself,” Menendez said after his primary win.

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Hugin has distanced himself from Trump throughout his campaign. He has said he is pro-choice, pro-marriage equality and “strongly support[s] equal pay for equal work.”

In the 2016 presidential election, Clinton took New Jersey with 55 percent of the vote; Trump won 41 percent.

Iowa could send youngest congresswoman ever to Washington

Abby Finkenauer, a Democratic candidate trying to unseat Republican incumbent Rod Blum in Iowa's 1st congressional district, is pictured on the grounds of the house in which she grew up in Sherril, Iowa, U.S. March 31, 2018. Picture taken March 31, 2018. REUTERS/Tim Reid - RC198EFBFE80

State Rep. Abby Finkenauer won the Democratic primary to take on incumbent Rep. Rod Blum, R-Iowa, in the fall. If she wins, she would be the youngest congresswoman elected.  (Reuters/Tim Reid)

State Rep. Abby Finkenauer won the Democratic primary to take on incumbent Rep. Rod Blum, a Republican, in the fall.

If she wins the general election, Finkenauer, 28, would be the youngest woman ever elected to Congress. Rep. Elise Stefanik, R-N.Y., currently holds that record as she was elected in 2014 at the age of 30.

Blum faces a tough re-election campaign in what Fox News has labeled a toss-up election. He ran unopposed in the primary, but a group of energized Democrats are vying to take him on in the general election. His seat is one targeted by the Democratic Congressional Campaign Committee.

“As I’ve said from day one, this is personal,” Finkenauer said in a statement after her win. “We started this campaign to stand up for families just like mine, who work hard and play by the rules but have the odds stacked against them.”

Fox News’ Adam Shaw and The Associated Press contributed to this report.

Kaitlyn Schallhorn is a Reporter for Fox News. Follow her on Twitter @K_Schallhorn.