Shortly before Indiana's Republican primary election in May, Pence endorsed Trump's rival, US Senator Ted Cruz of Texas.
Pence praised Trump at the time, but he compared Cruz to former Republican President Ronald Reagan and called him a "principled conservative."
Trump won the state anyway, and Cruz dropped out of the Republican race. Trump and Pence have since met to discuss the running mate position.
Pence has strong ties to billionaire donors Charles and David Koch, including current and former staff members who have worked for them.
After saying he was primarily self-funding his campaign during the Republican primaries, Trump has been holding fundraisers during the general election, with support from the Republican National Committee.
The New York businessman comes to the money race at a considerable disadvantage, however, compared with Democratic presidential candidate Hillary Clinton.
Pence sometimes describes himself as "a Christian, a conservative and a Republican, in that order."
Pence in 2015 signed a religious freedom law that critics said opened the door to anti-gay discrimination. When he was in Congress, he opposed repealing the military's "Don't Ask Don't Tell" policy on sexual orientation.
He also has pushed restrictive abortion regulations and has pushed for Congress to defund Planned Parenthood, a nonprofit women's health provider that performs some abortions.
He was a vocal opponent of the 2008 Wall Street bailout.
In September 2008, Pence, then a US House member, argued against the $US700 billion ($A920.27 billion) package to stabilise the US financial system, saying it would "nationalise almost every bad mortgage in America."
Pence also said the Dodd-Frank financial reform legislation passed in 2010 would hurt jobs. Trump has vowed to dismantle Dodd-Frank, though he has not said how he would replace it.
Pence opposed allowing Syrian refugees coming to the United States to settle in Indiana.
In November 2015, the governor directed state agencies to suspend the resettlement of Syrians there. A family that was supposed to arrive in December was instead sent to Connecticut.
A federal judge later ruled the order "clearly discriminates" against refugees from a particular country.
However, Pence tweeted disapproval in 2015 for plans to ban Muslims from entering the United States, an idea Trump has advocated. Pence called it "offensive and unconstitutional."