The battle for the Senate is tilted heavily in Republicans' favor. But there are glimmers of hope for Democrats.

The GOP advantage is largely due to Democratic successes in the last two elections of for this specific one-third of the Senate. The party did so well in 2012, during the re-election of President Barack Obama, and before that during the 2006 midterm swing against President George W. Bush, that they had won seat after seat beyond expectations in each instance. But after Republicans scored major gains and a Senate majority in 2014, and then managed to defend their position in 2016, the remaining portion of the Senate up this year would appear — at least on its face — to make a change of party control a big lift.

The fundamental nature of this year's Senate map puts Republicans in a position of fairly low risk. Of the 35 Senate seats that are up for election this year, Democrats (and the two Dem-aligned independents) hold a whopping 26 of them, to only nine seats for the Republicans. Furthermore, 10 seats are held by Democrats in states carried by President Trump in 2016, while only one Republican is from a state carried by Hillary Clinton.

Still, Democrats received a major bump with the shocking win of Sen. Doug Jones (D-Ala.) in last year's special election. That one victory achieved two aims: It brought the party to 49 seats, ever so close to a majority (Democrats now only need a net gain of two Senate seats in the 2018 midterms, instead of the much more daunting three seats they'd needed before) while also demonstrating that Democrats could win in red states.

Here are the 13 key races that will likely decide the fate of the Senate.

REPUBLICAN-HELD SEATS

Nevada: Sen. Dean Heller (R) vs. Rep. Jacky Rosen (D)

This is the one Republican-held seat in a state Hillary Clinton won in 2016 — making incumbent Sen. Dean Heller the number one target for Democratic hopes to make gains. Democratic Rep. Jacky Rosen is focusing on Heller's vote last year in the unsuccessful push to repeal the Affordable Care Act, after he had previously indicated his opposition to the GOP's quest to kill ObamaCare.

The most recent public poll was back in late July, putting Heller at 41 percent and Rosen at 40 percent.

Texas: Sen. Ted Cruz (R) vs. Rep. Beto O'Rourke (D)

This state has not elected a Democratic senator since 1988, with the re-election of centrist incumbent Lloyd Bentsen (who was simultaneously running for vice president on the ticket with presidential nominee Michael Dukakis — and they lost that race both in Texas and nationally). Still, lots of wags are focused on this race, thanks in part to Cruz's personal unpopularity. (Texas Republicans are trying to drive up O'Rourke's negatives, as well — though possibly with some mixed results.)

O'Rourke recently achieved viral status when he spoke in defense of protests by NFL players as an expression of free speech: "And I can think of nothing more American than to peacefully stand up, or take a knee, for your rights, any time, anywhere, in any place." In response, Cruz has accused O'Rourke of disrespecting the sacrifices of veterans.

And in a very interesting sign for a Senate seat in such a red state, President Trump has announced that he will be campaigning for Cruz. This is also quite the interesting turn, after they had spent the 2016 Republican primary season attacking each other, with Trump gaining the upper hand by nicknaming Cruz "Lyin' Ted," spreading a conspiracy theory about his father, and publicly insulting his wife's looks.

The RealClearPolitics poll average has Cruz with 45.8 percent, and O'Rourke at 41.4 percent.

Arizona (open seat): Rep. Martha McSally (R) vs. Rep. Kyrsten Sinema (D)

Republican Sen. Jeff Flake, who has become a very public critic of the Trump administration, announced his retirement at a time when polling showed that he would likely lose in a primary challenge from right-wing former state Sen. Kelli Ward. Instead, the Republican primary in August was won by Rep. Martha McSally, an Air Force veteran, who easily defeated Ward. The Democratic nominee is Rep. Kyrsten Sinema, who has touted her rise from poverty and childhood homelessness to graduating from college and serving in Congress.

The race is also historic in one sense: No matter who wins, Arizona will have its first woman U.S. senator.

It's looking a scrapper of a campaign, to determine who that will be, with McSally attacking Sinema for having protested the Iraq War in the early 2000s, while McSally was herself serving overseas.

Also key here is Trump's antagonism of Latino voters, which some have speculated could spur a sea change in the state, which Trump had only won by a margin of a little over three percentage points in 2016.

The most recent poll, from late July, had Sinema at 48 percent to McSally at 44 percent.

Tennessee (open seat): Rep. Marsha Blackburn (R) vs. former Gov. Phil Bredesen (D)

Republican Sen. Bob Corker, another notorious Trump critic, is retiring after two terms, in a deep-red state that may be competitive on account of some unique circumstances. First, Democrats have recruited a top-tier candidate in Bredesen, who last won his second term as governor with a whopping 69 percent of the vote back in 2006. But then again, that was a long time ago — can he do it again?

Blackburn has touted her support for (and personal endorsement from) Trump, a logical strategy in a state that Trump won with 61 percent of the vote in 2016. On the other hand, Trump's tariffs have become a sticky issue in the state, with Blackburn positioning herself as a critic, while Bredesen has called for limits on presidential power to impose tariffs.

The RealClearPolitics poll average has Bredesen with 45.0 percent, and Blackburn at 43.7 percent. The key thing to look out for: As we get closer to Election Day itself, will Blackburn be able to solidify Republican voters behind her?

DEMOCRATIC-HELD SEATS

Florida: Sen. Bill Nelson (D) vs. Gov. Rick Scott (R)

The perennial swing state, Florida narrowly voted for Trump in 2016, after having previously voted narrowly for Barack Obama in 2008 and 2012. And when there's a large swing state, with numbers in both population and geographic media markets, that means a lot of money will be coming in. Indeed, this is expected to be the most expensive Senate race of the year, thanks in part to the wealthy Gov. Rick Scott putting in over $20 million of his own money so far.

One possible feather that three-term Sen. Bill Nelson might have in his cap: the surprise nomination of Tallahassee Mayor Andrew Gillum as the Democratic gubernatorial candidate might help spur more African-American voter turnout, always a key for Democrats in diverse states.

The RealClearPolitics poll average has Scott with 46.5 percent, and Nelson at 44.8 percent.

Wisconsin: Sen. Tammy Baldwin (D) vs. State Sen. Leah Vukmir (R)

This was one of the key states that surprised everyone by voting narrowly for Trump in 2016. Recent polling, however, shows that Trump's disapproval is above 50 percent in the state, similar to the national averages.

Baldwin is running heavily on health care, and preventing Trump administration actions to weaken protections for pre-existing conditions. Vukmir has been touting her status as a military mom, while accusing Baldwin of being on "Team Terrorists" for opposing the confirmation of CIA Director Gina Haspel.

The RealClearPolitics poll average has Baldwin with 49.7 percent, and Vukmir at 41.7 percent.

North Dakota: Sen. Heidi Heitkamp (D) vs. Rep. Kevin Cramer (R)

This state gave 63 percent of its vote to Trump in 2016, making it a daunting task for even a well-known local Democrat to hold on to office.

Here, tariffs are again an issue, and Heitkamp is running on her support for health-care reform and protecting individuals with pre-existing conditions. Cramer, meanwhile, is running on his support for Trump, and has accused Heitkamp of having "become an enemy of our country, for crying out loud," by opposing Trump's trade policies.

The most recent public poll was all the way back in June, and it gave Cramer a lead with 48 percent to Heitkamp's 44 percent.

Montana: Sen. Jon Tester (D) vs. State Auditor Matt Rosendale (R)

This state voted 56 percent for Trump in 2016, making it a key target for Republicans this year. Two-term Sen. Jon Tester got his first big break early on, however, when Trump appointed GOP Rep. Ryan Zinke to be secretary of the interior — thus taking a major potential challenger out of play.

Tester is putting up his local brand, and a large number of ticket-splitting voters (the state also has a Democratic governor, who won re-election in 2016 at the same time as Trump's victory) versus Rosendale's strong support for the White House.

Republicans recently released an internal poll, claiming a narrow edge for Rosendale of 47 percent to Tester's 45 percent.

Missouri: Sen. Claire McCaskill (D) vs. State Attorney General Josh Hawley (R)

This red state voted 56 percent for Trump in 2016, with Republicans also sweeping other statewide races at the time. But things have taken a turn since then, with the resignation of disgraced Gov. Eric Greitens (R) in a sexual assault scandal, and the rejection by voters of a right-to-work measure against labor unions.

A recent public poll has the two candidates tied, at 47 percent each. It's anybody's race.

West Virginia: Sen. Joe Manchin (D) vs. State Attorney General Patrick Morrisey (R)

This state voted 68 percent for Trump, while Democratic Sen. Joe Manchin has touted his own conservative positions such as support for funding a border wall, and even gone so far as to say it was a "mistake" to support Hillary Clinton in 2016, due to her opposition to the coal industry. At the same time, he has touted his support for health-care reform, and the protection of pre-existing conditions as a key condition for his vote on Supreme Court confirmations.

And believe it or not, it's worked — at least so far — with public polling mostly showing Manchin ahead. A political action committee supporting Morrisey recently released an internal poll, to demonstrate some momentum — and even here, Manchin is reportedly ahead with 47 percent, to Morrissey's 40 percent.

Indiana: Sen. Joe Donnelly (D) vs. former state Rep. Mike Braun (R)

Trump won this state with 56 percent of the vote in 2016 — and it is also the home of Vice President Mike Pence.

As with other states, we see the issues of Trump's trade war and a local Democratic incumbent's proclaimed independence and bipartisanship — indeed, both candidates have ads featuring them shaking Trump's hand. Donnelly is also running on the issue of protecting health insurance coverage for pre-existing conditions, while Senate Republicans are set to air a TV ad featuring Pence himself, attacking Donnelly and urging a vote for Braun.

The most recent poll, from late August, put Donnelly ahead with 49 percent to Braun's 43 percent.

Minnesota: Sen. Tina Smith (D) vs. state Sen. Karin Housley (R)

A potential wild card: This seat is unexpectedly up in a special election, with Smith having been appointed to the seat by Gov. Mark Dayton last year after the resignation of Democratic Sen. Al Franken. Smith was previously elected as lieutenant governor on a ticket with Dayton, and before that she had been the governor's chief of staff. However, she has never run for an office by herself, thus making her a somewhat untested political commodity.

A recent poll has Smith ahead, with 44 percent support to Republican candidate Karin Housley's 37 percent. Smith also has another benefit: running alongside popular incumbent Democratic Sen. Amy Klobuchar, whose regular term is also up this year, and who is ahead of her own Republican opponent by a margin of 54 percent to 34 percent. President Trump's disapproval rating stands at 54 percent, making this favorable ground for Democrats.

New Jersey: Sen. Bob Menendez (D) vs. businessman Bob Hugin (R)

Another odd case of a vulnerable Democrat in a blue state: Democratic Sen. Bob Menendez went through a corruption trial from 2015 to 2017, ending in a mistrial due to a hung jury — after which one juror spoke out, saying that 10 out of 12 were in fact ready to acquit him. Then after a judge acquitted Menendez on some of the charges, the Justice Department gave up on plans to retry him and simply dropped all of the remaining charges.

Republican candidate Bob Hugin, a former pharmaceutical executive, has already spent over $15 million of his own money going after Menendez on ethics issues — while the Menendez campaign has gone after Hugin for the $280 million settlement his company had to pay to the FDA, and for raising drug prices.

A recent poll gave Menendez just 43 percent support, though still ahead of Hugin at 37 percent — and in a troubling figure, 49 percent believe that Menendez was involved in some kind of serious wrongdoing, against only 16 percent who say he wasn't. But at the same time, President Trump's 63 percent disapproval in the Garden State — much higher than Menendez's own disapproval figure of 47 percent — also makes Republican chances here an uphill climb, to say the least.

Menendez doesn't need New Jersey voters to love him. He only needs to make sure that they dislike Trump, and Republicans in general, even more than they might be looking askance at himself.