(CNN) After meeting with Muslim leaders in Saudi Arabia and visiting sacred sites in Jerusalem, President Donald Trump's tour of world religions concluded Wednesday at the Vatican, the Catholic Church's holy headquarters.

There, at the Apostolic Palace, Trump met with Pope Francis -- finally.

It's a meeting millions had been waiting for, an encounter between two of the world's most intriguing and complex characters: The holy man in white who preaches good news to the poor and the brash businessman in the dark suit who embodies American extravagance.

After months of talking -- and tweeting -- past one another, as well as a very public spat over international borders, the Pope and Presidentmet at last, with nary a barrier between them.

A boxing promoter might have been tempted to call it the "Sistine Showdown" or " Rumble in Rome." Churchmen, alas, chose more sober sobriquets.

"It will be a meeting without 'walls,'" the Rev. Antonio Spadaro, a close associate of the Pope, said a few days before the President's visit.

Walls, of course, were the subject of their famous feud.

Shortly after celebrating a large outdoor Mass at the Mexican border last year, Francis said that people who think only of building barriers instead of bridges are "not Christian." Trump dismissed the comments as "disgraceful" and called the Pope a pawn of the Mexican government.

It was catnip to a culture that feasts on conflict: A politician and Pope sparring in the middle of a heated presidential election. But neither man seemed eager to continue the clash . The Vatican said Francis' comments were "not a personal attack," and Trump said he "doesn't like fighting with the Pope."

Pope Francis walks past US First Lady Melania Trump and the daughter of US President Donald Trump Ivanka Trump at the end of a private audience at the Vatican on May 24, 2017.

Still, the Pope continued to condemn Trump-like political rhetoric, even if he never named Trump himself. The day before the presidential election, he warned Christians not to be tempted by "the false security of physical or social walls."

"Dear brothers and sisters," he said, "all walls fall. All of them. Do not be fooled."

After the election, several of Francis' closest American allies picked up the Pope's banner, sounding ready to lead an anti-Trump resistance.

"What keeps despots, dictators awake at night, what topples evil empires is the little person who goes into the square in the middle of the town in the dark of the night and scrawls on the wall, 'No,'" Cardinal Joseph Tobin of Newark, New Jersey, said earlier this month at a rally to support a Mexican immigrant threatened with deportation.

"And I want to say to you, we are the 'No' that God scrawls on the wall."

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Bishop Daniel Flores said his flock in the border town of Brownsville, Texas, is anxious about the anti-immigrant rhetoric coming from the highest levels of government. They wanted the Pope to say something about it to Trump.

"People here see the Pope as someone who defends the integrity of immigrants' identity," Flores said. "They are hoping, when he meets the President, that there may be some progress in understanding, especially in halting efforts to dehumanize the immigrant population."

Still, most experts said before the meeting they didn't expect Francis to take Trump to the woodshed -- or drag him to the confessional booth.

At a recent news conference, the Pope said he wouldn't judge Trump before their meeting or seek to convert him on political issues. Instead, he'd look for areas of agreement.

"Always there are doors that are not closed. Look for the doors that are at least a little bit open, enter and talk about common things and go on. Step by step."

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Trump, in his weekly address Friday, said he looked forward to "the honor" of meeting the Pope and discussing "how Christian teachings can help put the world on a path to justice, freedom and peace."

That's a slight misunderstanding of typical meetings between the Vatican and politicians, said Massimo Faggioli, a professor of Catholic history at Villanova University.

The Holy See, in addition to being the spiritual home of the Catholic Church, is a sovereign nation, with diplomats posted across the world, including in the United States.

"When the Vatican speaks to heads of state, they don't talk about religion," Faggioli said. They talk about global issues, such as human trafficking, the refugee crisis and the environment.

Finding common ground

Despite their awkward history, the Pope and President share some commonalities, Faggioli said, particularly their remarkable rises to power.

Trump's businesses descended into multiple bankruptcies before he recovered his financial footing and became a media star. Francis was exiled by his Jesuit community , a banishment that only ended when he was appointed a bishop. Trump is the first American without political or military experience to occupy the Oval Office. Francis is the first Latin American to sit in St. Peter's chair.

"They are both outsiders, both survivors of big challenges," Faggioli said. "Both of their careers were considered over at one point, and they came back."

In late 2013, Trump said he saw echoes of himself in the new pontiff.

"The new Pope is a humble man," Trump tweeted , "very much like me, which probably explains why I like him so much!"

Humble or not, Trump, like the Pope, presents himself as a voice for the voiceless, an enemy of elitism and a fighter for men and women forgotten by the march of modern globalism. And both are prone to an off-script spontaneity that often leaves aides scrambling to corral the consequences.

That's what makes Wednesday's meeting so unpredictable. No one knows what will happen. But we know a little about the agenda.

What will they talk about?

National security adviser Lt. Gen. H.R. McMaster said Trump's agenda includes religious freedom, cooperating with the Catholic Church in humanitarian missions and combating religious persecution and human trafficking.

Ivanka Trump, the President's daughter, will also meet with the Catholic community Sant'Egidio to discuss human trafficking, according to the White House.

The Pope often starts conversations on areas of agreement, said Spadaro, the Jesuit editor.

"Francis, the Pope of bridges, wants to speak openly with any head of state who asks him because he knows that in crises, there are no absolute 'good' or 'bad' people, but specific interests are always at play."

Those issues, other church experts said, could include abortion, euthanasia, religious freedom and the need to protect persecuted Christians, particularly in the Middle East, on which Francis and Trump share similar views.

But the Pope was also expected to raise several issues on which he and the President do not agree, church experts say, such as climate change and the plight of Syrian refugees. The Pope issued a lengthy encyclical warning of an imminent environmental collapse. Trump has called climate change a Chinese hoax.

And with an executive order, now contested in US courts, Trump has tried to bar Syrian migrants from entering the United States. The Pope, meanwhile, has welcomed several Syrian families who now live inside Vatican City.

At the same time, the Pope seems increasingly concerned about the saber-rattling rhetoric emanating from the United States and North Korea, warning that a military conflict on that scale could kill a "large part of humanity."

Disagreements aside, Francis will likely let Trump do most of the talking, said Austen Ivereigh, author of "The Great Reformer," a biography of Pope Francis. Above all, Francis wants to make a personal connection with the American President.

"He knows that Trump is an erratic and volatile person, and a good result of the meeting for Francis would be that he could later pick up the phone and say to Trump, 'Mr. President, hold on, or please think again.'"

Reading body language

Rep. Francis Rooney, Vatican ambassador from 2005-2008, said much of the statecraft occurs on the sidelines of the main event, in meetings between the countries' chief diplomats.

The Holy See has humanitarian missions in hundreds of countries, and often offers help in broaching difficult diplomatic situations. For instance, church leaders provided crucial connections between the United States and Cuba as they sought renewed relations.

After the Pope and President meet, the Vatican and White House will issue short and studiously vague statements about the topics they discussed. No one except the Pope, the President and their two translators will know what was said behind closed doors.

But everyone can read their body language at the beginning and end of the meeting, when a few photojournalists are allowed in the room.

"Everyone will be looking at that initial exchange," said the Rev. Timothy Kesicki, president of the Jesuit Conference of Canada and the United States. "Was it warm or cool? Was there chemistry or awkwardness?"

The smiles between President Obama and Pope Francis were seen as a sign that they liked one another.

The length of the meeting has often been considered a gauge in the goodwill between popes and presidents, but it may not be much help on Wednesday. Francis is scheduled to deliver his weekly address in St. Peter's Square shortly after his time with Trump, which may curtail the encounter.

Francis will probably never say anything publicly about his meeting with the President, Ivereigh said, even if Trump tweets misleading statements about it. If the Pope does decide to respond, he has a pretty big pulpit -- and Twitter following -- of his own.