With the 2020 Democratic primary virtually decided, the search—and campaign—for the next veep is officially on.

And Joe Biden's already got a head start: He's been vetting potential vice presidential nominees since early April. (CNN)

Biden promised to pick a woman as his running at the March Democratic debate. Here are some of the frontrunners.

Minnesota Sen. Amy Klobuchar is being eyed by many as the most likely and "logical" choice for Biden's VP.

Klobuchar propelled Biden to a surprise victory in Minnesota after she endorsed him on the eve of Super Tuesday.

In 2018, Klobuchar won reelection by 24 points in Minnesota, where Hillary Clinton eeked a win with 1.5 points in 2016.

David Byler, WaPo: "She knows how to win swing voters and get liberal legislation through Congress...."

Sen. Kamala Harris is another favorite; she would be the first Black, Asian-American woman on a presidential ticket.

Biden told reporters in Dec.: "She can be the VP. She can go on to be a Supreme Court justice. She can be an AG."

Biden and Harris also share a personal bond: Harris worked with and was friends with Biden's late son, Beau Biden. (CNN)

Biden told CNN, "She knew Beau, she knows me." Biden has also been urged by allies to choose a woman of color as VP.

If you can remember, in 2019, Biden privately met with Stacey Abrams before announcing his 2020 run.

Since then, Abrams' name has floated around as a potential 2020 candidate and vice presidential pick.

Abrams lost her 2018 gubernatorial race by 1.4 points. In the meantime, she's focused on her voting rights initiative.

By now, everyone knows Mich. Gov. Gretchen Whitmer, who delivered the response to the State of the Union this year.

In 2018, Whitmer was elected governor by 9 points in Michigan—a state that Trump won in 2016.

Whitmer campaigned for Biden in Michigan, where he won all of the state's 83 counties in the primary.

Whitmer is still in her first term as governor, so it's unlikely she'll accept an offer.

Wisconsin Sen. Tammy Baldwin would not only be the first woman VP, but also the first openly LGBTQ VP.

Biden campaigned for Baldwin's reelection in 2018, a race that she won with 55%. Wisconsin went for Trump in 2016.

But, all eyes are on the Senate and, unlike Harris in California, Baldwin's seat could be at risk in a special election.

Sen. Elizabeth Warren endorsed Biden this week and told Rachel Maddow that she would accept a VP position if offered.

Biden has already adopted Warren's bankruptcy and student loan plans. It's likely that he'll include her in his cabinet.

A March Economist/YouGov Poll put Warren as the top pick for VP at 27%. Trailing her was Harris at 18%.

Former national security advisor Susan Rice, who served for the entirety of the Obama administration, has also come up.

Bill Scher, Politico: "No one could...question her qualifications to assume...the presidency if necessary."

Illinois Sen. Tammy Duckworth would, along with Harris, become the first Asian-American woman veep if chosen.

Her personal story as an Iraq War veteran could resonate with many. She's also another Midwesterner with broad appeal.