Veepstakes 2016: A Look at the Potential Vice Presidential Picks for Donald Trump and Hillary Clinton Who the candidates might choose as their No. 2

 -- ABC News is tracking all the developments in this year's "veepstakes" -- the selection of running mates by presumptive Republican nominee Donald Trump and presumptive Democratic nominee Hillary Clinton.

The list below represents potential vice presidential picks for both candidates. It is not exhaustive, but instead captures what we consider to be the "top tier" of possible choices based on ABC News’ reporting and analysis.

The ABC News Political Unit will update the list -- adding and subtracting names -- as reporting and new developments warrant.

Here's a look at ABC's 2016 veepstakes list:

Donald Trump's Potential Running Mates

Scott Brown

Current position: Political contributor for Fox News Channel and Trump surrogate

Veep cred: Brown served as a U.S. senator from Massachusetts for two years after several years in the Massachusetts state Senate and House. Before his elections to public office, Brown worked as a defense attorney.

Potential pitfall: Lost two elections in a row. He failed to hold onto his U.S. Senate seat in the 2012 election, losing to now-Sen. Elizabeth Warren, a Democrat. Then in 2014, he ran for a U.S. Senate seat in New Hampshire, only to lose to Democratic Sen. Jeanne Shaheen and to face accusations of being a “carpetbagger.”

What he has said about the veepstakes: “Nah, that’s never going to happen. It’s like sitting around at a bar and talking about who’s going to win the World Series next year,” Brown told ABC News back in February.

Current position: New Jersey Governor

Veep cred: Christie has served as governor of New Jersey since 2010. Before that, he served for six years as U.S. attorney for New Jersey, a post to which he was appointed by former President George W. Bush.

Potential pitfall: According to a Quinnipiac University poll released in May, 72 percent of New Jersey voters oppose the idea of Christie as Trump’s running mate while 18 percent are in favor. In addition, the poll delivered Christie his lowest-ever approval rating, with 64 percent of voters disapproving of the job he is doing as governor and 29 percent approving.

What he has said about the veepstakes: “You don't get to make those determinations," Christie told reporters in Mendham Township, New Jersey, on June 7, 2016. "I've had no conversations about it."

Mary Fallin

Current position: Oklahoma Governor

Veep cred: Fallin got her start in politics in 1990 when she was first elected to the Oklahoma House of Representatives. She subsequently served as lieutenant governor for three terms, and in the U.S. House of Representatives. She announced her run for governor in 2009 and took office in 2011. She is the first woman to serve as Oklahoma’s governor.

Potential pitfall: Fallin came under fire after her top lawyer approved a planned execution to go forward in April, even though prison officials received the wrong drug.

What she has said about the veepstakes: “My first and foremost goal right now is to finish our legislative session,” Fallin said on May 4, the day she endorsed Trump. “But if I were to receive a call that said, ‘I need you to help make America great again,’ I’d be happy to take that call.”

Newt Gingrich

Current position: Former House Speaker

Veep cred: Gingrich was in public office for nearly 20 years, serving as the U.S. representative for Georgia's 6th District, as House minority whip and as speaker of the House.

Potential pitfall: Gingrich, 72, is no spring chicken and may have trouble appealing to younger voters.

What he has said about the veepstakes: “Well, I would certainly talk about it, Gingrich told Fox News on May 11, 2016. “I wouldn’t turn it down automatically.”

Mike Pence

Current position: Indiana Governor

Veep cred: The Indiana native has served as governor since 2013. Before winning election as his state's chief executive, Pence represented Indiana’s 6th Congressional District in the U.S. House of Representatives from 2001 to 2014. He also served as a chairman of the House Republican Conference and is a respected conservative voice.

Potential pitfall: Pence’s approval ratings have fallen in recent months -- a drop many linked to his passing of the Religious Freedom Restoration Act. Critics argued the controversial bill would allow businesses to discriminate against those in the LGBT community. Pence later signed an updated version of the bill that banned businesses from discrimination based on sexual orientation.

What he has said about the veepstakes: "I have no interest in that," Pence said in May about the possibility of being picked as Trump’s No. 2. "I’m going to stay focused on the future of the people of Indiana.”

Current position: U.S. Senator from Alabama

Veep cred: Sessions was elected to the U.S. Senate in 1996 and has held the position since. He was the first senator to endorse Trump and also serves as the candidate's adviser on immigration and foreign policy.

Potential pitfall: Though Sessions was ranked by the National Journal as one of the most conservative senators on Capitol Hill, he is also considered part of the Washington establishment that Trump often rails against.

What he has said about the veepstakes: “Don’t bet any money on me,” the Alabama senator told reporters outside the Senate chamber on April 7, 2016.

Hillary Clinton's Potential Running Mates

Julian Castro

Current position: Secretary of the U.S. Department of Housing and Urban Development

Veep cred: Castro, a former mayor of San Antonio, and in 2012 became the first Latino to deliver the keynote address at a Democratic National Convention. Castro, 41, appeals to young voters and Hispanic voters.

Potential pitfall: Because Castro is so young, rivals might try to peg him as inexperienced.

What he has said about the veepstakes: "That's not going to happen,” Castro said in an interview with CNN on May 10, 2016. Castro also said he is not being vetted, and he has not heard from the Clinton campaign.

Tim Kaine

Current position: U.S. Senator from Virginia

Veep cred: Kaine has a strong resume, having served as a mayor, governor and a U.S. senator. Kaine also serves on the Senate Foreign Relations and Armed Services committees and is fluent in Spanish.

Potential pitfall: Accepted more than $160,000 worth of gifts over the eight years he served as the lieutenant governor and governor of Virginia.

What he has said about the veepstakes: “Don’t believe the hype, Andrea,” Kaine told MSNBC’s Andrea Mitchell on May 10. “I’m just doing my work here in the senate and in Virginia. My highest and best use is really in Virginia because I do think that will be a critical state this November, and I’m going to do everything I can to help Hillary win.” Kaine also said the only role he has with the campaign “right now” is “campaigning and helping them win, especially in Virginia.”

Tom Perez

Current position: U.S. Secretary of Labor

Veep cred: Perez previously served as the Assistant Attorney General for Civil Rights at the U.S. Department of Justice. Before that, he served as secretary of Maryland's state Department of Labor, Licensing and Regulation, and as a member of the Montgomery County Council.

Potential pitfall: Perez has worked at the local, state and national levels, but some may say he lacks foreign policy chops. However, the biggest pitfall Perez may face is potential criticism over his role in the Supreme Court’s dismissal of the case, Magner v. Gallagher -- which was an issue of contention in his 2013 confirmation hearing.

What he has said about the veepstakes: "I have had no conversations about that, and I am glad about that, because I continue to do my day job, and in my spare time, I'm helping Secretary Clinton get elected," Perez said on a May 12 press call.

Mark Warner

Current position: U.S. Senator from Virginia

Veep cred: He is serving his second term in the U.S. Senate and before that served as the governor of Virginia.

Potential pitfall: In 2014, Warner was involved in a federal investigation following the resignation of Virginia State Sen. Phillip Puckett. Sen. Puckett's son, Joseph Puckett, claimed Warner discussed job opportunities for the state senator’s daughter in an effort to dissuade the elder Puckett from quitting the evenly divided senate.

What he has said about the veepstakes: “I think the best value I can add is in the United States Senate,” Warner told local station WJHL in an interview on May 6, 2016.

Current position: Senior U.S. Senator from Massachusetts

Veep cred: An expert on bankruptcy regulation and a former professor at Harvard Law School, Warren has a popular following in anti-establishment circles in the Democratic Party and could unify voters on the left by helping to bring former supporters of Bernie Sanders on board with a Clinton presidency.

Potential pitfall: Warren’s hostility toward Wall Street reflects the sort of rhetoric that helped Sanders gain traction on the campaign trail, which could alienate major donors who want to remain supportive of the Democratic Party and Clinton’s campaign.

What she has said about the veepstakes: In September, Warren said after a local event in Boston that the vice presidency is “something I’m not talking about,” according to the Associated Press. Clinton created a buzz in early June when she told POLITICO that Warren is “eminently qualified for any role.”