Vice President Kamala Harris and former President Donald Trump dueled it out during their first presidential debate on Tuesday and, with the debate behind them, they are now traveling to different swing states where they will get the chance to speak directly with voters.

Trump has his sights set on Arizona, where he will hold a rally in Tucson, while the Harris team is heading to North Carolina, where she's scheduled to hold events in Charlotte and Greensboro.

Arizona and North Carolina are both considered among prized battlegrounds for the 2024 election and the opposing campaigns undoubtedly understand that securing either will help expand their narrow paths to victory in a closely fought presidential race.

Thursday’s events come after both candidates spent Wednesday commemorating those who lost their lives during the terror attacks on Sept. 11, 2001.

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Democratic presidential nominee, U.S. Vice President Kamala Harris, U.S. President Joe Biden, former NYC Mayor Michael Bloomberg, former U.S. President Donald Trump and Republican vice presidential nominee, U.S. Sen. J.D. Vance, R-OH, all attend the annual 9/11 Commemoration Ceremony at the National 9/11 Memorial and Museum on September 11, 2024 in New York City.  (Michael M. Santiago/Getty Images)

Polling experts say only a handful of battleground states will ultimately decide the outcome of the election and the candidates’ respective destinations give insight into their strategies.

Harris hit the ground running in her first post-debate campaign push, releasing a new ad that featured quotes from their showdown.

The current vice president also announced that she would be returning to North Carolina for a pair of rallies.

Trump won North Carolina in both of his previous White House bids. The former president held rallies throughout the state last month and Republicans have been confident about his chances to win the state for a third time.

However, Trump's 2020 margin of victory in the state was just 1.3 percentage points, his narrowest win of any state that year.

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The Harris campaign’s eagerness to return to North Carolina points to their hope that its diversifying population will give them a chance to flip the state this go around. Harris's campaign said Thursday's trip will be her ninth to the state this year.

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Historically, Democrats haven't won North Carolina's electoral votes since 2008, when former President Obama was elected for the first time.

Registered independents — also known as unaffiliated voters — are the state’s largest voting bloc, so it is widely up for grabs.

A state Supreme Court ruling this week affirming that Robert F. Kennedy Jr. must be removed from North Carolina ballots could bring additional votes Trump’s way. Kennedy, a lifelong Democrat who was running as an Independent, endorsed Trump in the race.

Historically, Republicans have dominated North Carolina in recent years and the state has voted red in 10 of the last 11 presidential elections (Obama won the state in 2008).

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In Arizona, the political trend is similar — with one major exception.

While Trump won Arizona in 2016, he lost it in 2020. Republicans have won Arizona in nearly every presidential election since World War II, but President Biden eked out a narrow victory in 2020.

Trump and Harris on debate

US Vice President Kamala Harris, right, and former US President Donald Trump shake hands during the second presidential debate at the Pennsylvania Convention Center in Philadelphia, Pennsylvania, US, on Tuesday, Sept. 10, 2024. (Getty Images)

More recently, the state has only voted for the Democratic presidential nominee in two of the last 18 elections (Clinton in 1996 and Biden in 2020).

Arizona was particularly tumultuous for Trump in 2020 as he previously clashed with the late U.S. Senator and 2008 Republican presidential nominee John McCain.

Republicans still outnumber Democrats in Arizona, but a third of voters are independents.

Trump in New York City

Former U.S. President Donald Trump and Republican vice presidential nominee, U.S. Sen. J.D. Vance, R-Ohio, visit with firefighters outside FDNY Engine 4/Tower Ladder 15 fire house in lower Manhattan on the 23rd anniversary of the 9/11 terror attacks on September 11, 2024, in New York City.  (Spencer Platt/Getty Images)

Wednesday’s somber display provided respite from partisan politics in the high-speed campaign season.

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At a fire station in Shanksville, Pennsylvania, close to where United Airlines Flight 93 crashed after passengers fought back against their hijackers, Trump met with locals. Biden and Harris visited the same fire station earlier in the day.

Trump and Harris met in-person later the same day, when both traveled to Manhattan for another 9/11 ceremony.

The Associated Press contributed to this report.