Here are the results as they are coming in:
Pennsylvania is a must-win state for Democrats if they want to take back the House, CBS Pittsburgh money and politics editor Jon Delano told CBSN Tuesday. President Trump turned the state red in 2016 and it has for years been overwhelmingly Republican in the House, but new districts have Democrats hopeful the state is in play.
Four-term U.S. Rep. Lou Barletta, a staunch supporter of Mr. Trump who first got national notice as a small-city mayor for his attempted crackdown on illegal immigration, on Tuesday won the Republican nomination for U.S. Senate in Pennsylvania.
Barletta had paid little attention to his Republican rival, state Rep. Jim Christiana, during the primary campaign. Instead, he focused his attacks on the candidate he hopes to unseat in the fall, two-term Democratic Sen. Bob Casey.
Barletta is a favorite of Mr. Trump, whom Barletta endorsed in 2016. Mr. Trump asked Barletta to run for Senate, and the president is expected to visit Pennsylvania to campaign for him.
Casey, who was unopposed for the Democratic nomination, has opposed Mr. Trump's Supreme Court pick, many of his highest-profile nominees and the GOP tax-cutting law. He is among 10 Democratic senators seeking re-election this year in states won by Mr. Trump, making Casey a target for Republicans.
Mr. Trump edged Democrat Hillary Clinton by less than 1 percentage point in Pennsylvania in 2016's presidential election. Republicans control the Senate, 51-49, and defeating Casey would give Republicans one more vote favorable to Mr. Trump to help advance the president's agenda. But it is a tall order.
Casey, the son of a late former governor, has strong name recognition and has won five statewide elections, including two as auditor general and one as state treasurer. He also has a huge cash advantage, with about $10 million in the bank at the end of April, compared with Barletta's $1.3 million.
Casey, 58, is popular with labor unions and backed former President Barack Obama's signature policies.
Barletta, 62, won his House seat during the Republican midterm wave of 2010, catapulted by the attention he received while mayor of Hazleton for attempting to use local laws to crack down on immigrants in the city who had entered the country illegally.
In the gubernatorial race, Pennsylvania state Sen. Scott Wagner will run against Democratic Gov. Tom Wolf after winning the GOP primary, CBS Philadelphia reports. Wagner defeated two first-time candidates from the Pittsburgh area, Paul Mango and Laura Ellsworth, surviving weeks of Mango's sharp-elbowed attack ads that painted Wagner as sleazy, greedy and a "deadbeat dad."
Pennsylvania's lieutenant governor has become the first holder of the office to lose in a primary election.
John Fetterman won the five-way Democratic Party primary race for lieutenant governor Tuesday, beating incumbent Mike Stack.
The Braddock mayor's victory means he will run on a ticket with Gov. Tom Wolf in the fall. Pennsylvania first started allowing lieutenant governors to serve a second term in the 1970s.
Fetterman had made a failed bid in 2016 for the U.S. Senate. Fetterman -- "America's Coolest Mayor" -- wasfor "Sunday Morning" in 2010.
Stack, a former Philadelphia state senator, has had a chilly relationship with Wolf in their first term together. Wolf last year ordered an investigation into the treatment of state employees by Stack and his wife and stripped Stack of state police protection.
For the candidates battling for congressional seats, they will all be chosen, for the first time, based on a new congressional map that the state Supreme Court said corrects GOP gerrymandering. Two local incumbent House Democrats from Pennsylvania have turned back primary challenges.
Dwight Evans, in his first full term, will face Republican Bryan Leib in the November general election. Brendan Boyle will face Republican David Torres. Evans and Boyle represent heavily Democratic districts in Philadelphia.
"I think it's great that we are finally doing something about gerrymandering and I hope this makes more people go out and vote because their votes actually count now," said Diane Dalto.
It's still early and unclear if the new map is affecting voter turnout, but it has created some interesting races.
Several incumbent candidates who are seeking re-election, like Congressman Dwight Evans, have to fight for re-election in a new district because of the new map.
Evans will still likely regain his seat, but under the new map, analysts say some Republican seats may be up for grabs.
"I'm hoping to see the tide swing," said Karren Knowlton.
Lincoln City Councilwoman Jane Raybould won the Democratic primary to try and unseat Republican Sen. Deb Fischer, a tough prospect in overwhelmingly conservative Nebraska. Raybould, who ran unsuccessfully for lieutenant governor in 2014, helps run a Nebraska grocery store chain founded by her late father. She was the best-financed Democrat in the race.
The other Democrats were Frank Svoboda, a retired farmer, attorney and judge from Lincoln; Larry Marvin, a retired real estate broker from Fremont; and Chris Janicek, of Omaha, who owns a specialty cake business.
Fischer easily defeated four GOP primary challengers and enjoys a substantial fundraising advantage and statewide name recognition. Her primary challengers were Jack Heidel, a retired math professor from Omaha; Dennis Frank Macek, a writer and retired air conditioning technician from Lincoln; Jeffrey Lynn Stein, a professional photographer from Omaha; and Lincoln businessman Todd Watson.
Libertarian Jim Schultz ran unopposed for his party's nomination.
In the gubernatorial race, Republican Gov. Pete Ricketts handily won the party's nomination to seek a second four-year term. He now faces state Sen. Bob Krist of Omaha, a former Republican and independent who joined the Democratic Party in February. Krist has pitched himself as a less partisan alternative to Ricketts who would work more collaboratively with the Legislature.
Ricketts ran against Krystal Gabel of Omaha, a registered Republican who has volunteered to create the Legal Marijuana Now Party of Nebraska.
Democrats Vanessa Gayle Ward, an Omaha community activist, and University of Nebraska at Omaha instructor Tyler Davis were also seeking the nomination in their first bids for public office.
Former state Sen. Russ Fulcher on Tuesday won the Idaho Republican crowded and competitive primary in the 1st Congressional District.
"It is an honor folks. Because when you invest your faith - in me, in this case - to represent you, every time I say a word, every time I cast a vote, I want you to know I take that very, very seriously," Fulcher said during his victory speech in Boise. "We're here because we have the same faith. We're here because we have the same Republican principals."
The district, whose voters strongly backed President Trump in 2016, is being vacated by Republican Congressman Raul Labrador, who unsuccessfully ran for Idaho governor rather than run for re-election.
The 56-year-old Fulcher originally filed to run for Idaho's open gubernatorial seat nearly a year ago. Fulcher instead jumped into the congressional race, reasoning that he and Labrador should serve in complimentary roles.
Fulcher failed to win the GOP gubernatorial primary in 2014 with a narrow loss to Gov. C.L. "Butch" Otter.
Fulcher beat six other Republicans in Tuesday's primary, gaining 43 percent of the GOP primary vote in early returns with more than two-thirds of precincts reporting. His opponents included former Lt. Gov. and former Attorney General David Leroy, first-time candidate Michael Snyder and state Reps. Luke Malek and Christy Perry.
He will face Democrat Cristina McNeil in the November general election.
Meanwhile, when former state Rep. Paulette Jordan, 38, won her primary, she became the first woman to be the Democratic gubernatorial nominee in Idaho. If she wins the general election, Jordan, a member of the Coeur d'Alene Tribe, would not only be the first woman to serve as Idaho governor but also the first Native American woman to serve in that position in any state.
But she faces a difficult race: Idaho hasn't elected a Democratic governor since 1990, and the Republican Party now controls a supermajority on all federal, state and legislative seats.
Lt. Gov. Brad Little, 64, a rancher who has spent the past 16 years in elected office, secured the GOP nomination. He's the pick of Republican Gov. C.L. "Butch" Otter, who decided not to seek a fourth term.
State Rep. Knute Buehler has emerged from a crowded primary to capture the Republican nomination for Oregon governor.
Buehler, who ran for secretary of state in 2012, was the most centrist of the Republican front-runners. He was among 10 GOP candidates in the primary.
However, Democratic Gov. Kate Brown remains the favorite to win in November. Brown became governor in 2015 upon the resignation of Gov. John Kitzhaber following an ethics scandal, and she won a special election in 2016.
Oregon is among eight states where Democrats control the governorship and both houses of the state legislature. Voters who identify as Democrats also outnumber their Republican counterparts by more than 9 percentage points.