The church’s attention now turns to its future.

At the funeral, heads of state, royals and religious leaders sat with an array of Catholic prelates in brilliant red robes around a closed cypress coffin holding the body of Francis, who died on Monday at age 88. Atop his coffin, the pages of an open gospel fluttered in the breeze.

The Vatican said that more than 250,000 people participated in the funeral, with the faithful spilling out of St. Peter’s Square and streaming down the long avenue to the Tiber River. In the previous days, a similar number waited on long lines to say farewell to Francis, whose body was dressed in red vestments and scuffed black shoes, as he lay in state before the basilica’s altar.

The papal coffin was then loaded into a customized white vehicle, known as the popemobile, which drove through Rome, past crowds of people with their hands aloft and chanting “great,” to the papal basilica of St. Mary Major. There, Francis was being buried during a private ceremony in a tomb with a one-word inscription: “Franciscus.”

Here is what else to know:

• Simplified ceremony: Francis last year had approved guidelines to make his funeral a less grand affair than those of his predecessors, reflecting his view of the pope as a humble pastor rather than a powerful figure. The centuries-old rites, however, still involved Catholic pageantry and 250,000 participants, the Vatican said. Accompanying the Mass were the sober melodies of Gregorian chants, sung by the pope’s personal choir.

• Remembering Francis: Cardinal Giovanni Battista Re, in a homily on Francis’ legacy, called him “a pope among the people” but avoided obvious political overtones. Bible readings that Francis chose for the ceremony affirmed Christian messages of hope and inclusivity.

• Choosing a successor: The focus now turns in earnest to the election of the next pope by the College of Cardinals at a conclave to begin in May. Several names have surfaced as possible successors.

Emma Bubola, John Yoon and Isabella Kwai contributed reporting.

On Tuesday, the day after Francis died, the cardinals started holding general congregation meetings behind Vatican walls. They discussed scheduling and logistics for the days leading up to the conclave, but also the issues, priorities and personalities they wanted highlighted.

Those meetings will continue in earnest on Monday, when most of the voting-age cardinals — those younger than 80 — have arrived in Rome. To expand the geographic scope of the church, Francis named cardinals in countries he said were at “the peripheries” — those that traditionally didn’t have them.

As a result, many within the College of Cardinals do not know one another. The twice-daily meetings, filled with short speeches but also informal conversations, will be an opportunity for those voters to become more familiar with one another, feel each other out and gauge priorities, agendas and charisma.

Over the next week, blocs will take sharper shape, favorites will rise and fall and questions about the direction of the church — whether to follow, reverse or leap ahead of Francis’ footsteps — will come to the fore.

The beginning of the conclave usually signifies the end of the campaign trail for the papacy, and recent elections have been relatively quick. But if there is no consensus, or if favorite candidates don’t secure the needed two-thirds majority among the voting cardinals, the conclave can become its own electoral season.

But all of this will take place in customary secrecy.

Mr. Trump? He was wearing blue.

And not even dark, midnight blue, but a clear, sapphire-like blue, with matching tie. Amid all the black and Cardinal red, it popped out like a sign.

The choice did not grossly violate the dress code for the event (which reportedly called for a dark suit with a black tie for men). Prince William also appeared to be wearing blue, though a shade closer to navy, and former President Joseph R. Biden Jr. wore a blue tie. But Mr. Trump’s look certainly skirted the edges.

It did not go unnoticed online, where social media users recalled that Mr. Trump had previously criticized President Volodymyr Zelensky of Ukraine for not wearing a suit to a meeting in the Oval Office in February, appearing to see it as a sign of disrespect. (At the pope’s funeral, Mr. Zelensky, who met privately beforehand with Mr. Trump, wore a black military-style jacket and black pants.)

Asked to comment on Mr. Trump’s choice, Karoline Leavitt, the White House press secretary, said, “The president looked great and presidential alongside our stunning first lady, who was, as usual, dressed perfectly for the occasion.”

Steven Cheung, the White House communications director, chided those who criticized Mr. Trump, saying, “The president and first lady honored the life and service of Pope Francis, and those who try to distract from that should be ashamed of themselves.”

For someone as keenly aware of the power of appearance as Mr. Trump, the suit was probably not a chance decision. Not, for example, a case of there being no clean dark options packed on Air Force One. Melania Trump, after all, was wearing a black coat (from Italian designers Dolce & Gabbana) and black veil, much like Brigitte Macron and Jill Biden.

And Mr. Trump owns a dark suit — he wore one to former President Jimmy Carter’s funeral in January.

But in this case, black might not have served his purposes. By contrast, Mr. Trump’s choice of deep sea blue was both immediately recognizable and seemed fully in line with his desire to telegraph that he is playing by no one’s rules but his own. Yet another effort to redefine old terms of engagement as he sees — well, fit.

In a strong, resonant voice before the many thousands of mourners who had gathered in St. Peter’s Square in Vatican City, Ms. Gussie read from the Acts of the Apostles 10: 34-43, a Bible verse that Francis chose for the service and that holds large significance for Catholics.

Ms. Gussie, 28, grew up in Florida, and graduated from Mount St. Mary’s University in Maryland with a degree in theology, according to her LinkedIn profile. She began working in Rome in 2019, according to her profile, and last October joined Vatican News — a news agency that Francis created to bolster news coverage of the church and the Vatican.

“I’m really happy to be here because it’s a great way to say goodbye to Pope Francis,” Ms. Gussie said on social media outside St. Peter’s Basilica on Saturday morning before the Mass. She added that her last memory of Francis was from her birthday. “He gave me a little blessing,” she said. “It’s really a special way to spend my birthday.”

She said it had been difficult to see Francis grow frail in his final days, “but he gave everything until the end.”

With the first papal transition in more than a decade underway following the death of Pope Francis, who was laid to rest on Saturday, here are some terms to know:

Conclave

This is the meeting of cardinals, set to begin next month, that will elect the next pope. The word comes from the Latin “with key,” and refers to the isolation imposed on the men (and they have always been men) as they make their decision inside the Vatican. They cannot leave the conclave except in rare cases, and phones, the internet and newspapers are not allowed.

The cardinals vote by secret ballot until a two-thirds majority is reached, and a new pope is elected. The process was recently dramatized in the movie “Conclave,” which papal experts said presented a fairly accurate depiction. (The New York Times has written about some of the possible contenders.)

College of Cardinals

Cardinals, known as the “princes of the church,” are the second highest ranking Catholic prelates, and together they are known as the College of Cardinals. There are 252 cardinals, appointed by the pope to assist and advise him on Church affairs, and when a pope dies, it falls to the college to choose a successor.

The word cardinal comes from the Latin “cardinalis,” which means “serving as a hinge.”

The group is led by a dean, a position currently held by Giovanni Battista Re, a 91-year-old Italian who has spent most of his career serving in the Roman curia. He will preside over the meetings that lead up to the conclave but will not attend the gathering, as only cardinals under the age of 80 are eligible to vote for pope.

Camerlengo

The camerlengo, appointed by the pope before his death, is a cardinal who administers the Vatican from the moment the pontiff dies until a successor is elected, and who oversees many of the tasks of the transition.

His duties include removing the pope’s ceremonial ring — known as the fisherman’s ring — after his death, sealing his study and bedroom and presiding over his internment.

The Italian word comes from the Medieval Latin “camarlingus,” which means chamberlain. The position is currently held by Cardinal Kevin Joseph Farrell, a 77-year-old American who was born in Ireland.

Sede vacante

This is the period between pontiffs and comes from a Latin phrase meaning “the seat is empty.” During this time, with the camerlengo serving as the Vatican’s de facto administrator, the College of Cardinals keeps general oversight of the Church, but is not allowed to make any major decisions.

The longest sede vacante, according to the historian Salvador Miranda, was more than two years and seven months, the result of infighting between French and Italian factions of the cardinals, and ended in 1271 with the election of Gregory X.

White smoke

After rounds of voting in the conclave, the ballots are burned. Wisps of smoke emerge from a chimney above the Sistine Chapel, and onlookers gathered outside watch for a sign that the cardinals have made a decision

If the smoke is colored black, it means they are still deadlocked. White smoke means a new pope has been elected. Chemicals are used to change the color, although in 2005, the Vatican also began ringing the bells of St. Peter’s Basilica to confirm that a decision had been made.

‘Habemus papam’

When a new pope is chosen, he emerges, dressed in a white cassock, on a balcony of St. Peter’s Basilica. A senior cardinal stands with him and proclaims, “Habemus papam,” a Latin phrase meaning, “We have a pope.”

Only Prime Minister Giorgia Meloni of Italy and President Javier Milei of the pope’s native Argentina had priority seating toward the front.

President Emmanuel Macron of France sat across an aisle from President Trump, and Melania Trump, the first lady, and the two presidents shook hands at one point in the service. Former President Joseph R. Biden Jr., a Catholic, sat farther away with Jill Biden, the former first lady.

Crowds watching on big screens around the square applauded when President Volodymyr Zelensky of Ukraine took his seat. Leaders from Africa and Asia, regions where the Catholic Church is growing, also took their seats, including President William Ruto of Kenya and President Droupadi Murmu of India.

Other royals who aren’t heads of state, including Prince William, sat in a group just in front of visiting government ministers and other dignitaries.

Away from the world leaders, among the crowds, Julian Assange, the founder of WikiLeaks who was imprisoned after his website published secret government documents in the 2010s, paid tribute to Francis with his family.

“Now Julian is free, we have all come to Rome to express our family’s gratitude for the Pope’s support during Julian’s persecution,” read a message on social media attributed to his wife, Stella Assange. The post said that the pope had written to Mr. Assange while he was in prison.

Paul III’s funerary monument for Paul III, who died in 1549, was designed by Guglielmo della Porta and was moved to its spot by Bernini himself. It is a bronze counterpoint of sorts to Bernini’s own monument for Urban VIII, who died in 1644.

The two popes “look at each other,” Pietro Zander, the basilica’s head of artistic heritage, said at a news conference this month. He added that restorers had decided to bare the breast of Bernini’s sculpture of Charity, which had been covered centuries before.

One of the most elaborate papal tombs designed for St. Peter’s never made it there. Michelangelo's Funerary Monument for Pope Julius II, with his famous statue of Moses, ended up being installed in Rome at the church of San Pietro in Vincoli, after Pope Julius, who died in 1513, shifted his attention to the ongoing construction of St. Peter’s.

Francis’ two predecessors, John Paul II and Benedict XVI, opted for considerably plainer tombs. John Paul, who died in 2005, rests in a decorated sarcophagus-type tomb in the right nave of the Basilica. Benedict, who died in 2022, rests below a plain marble slab in a tomb in the Vatican Grottoes, underneath the Basilica.

Francis asked to be buried across town at the Papal Basilica of Santa Maria Maggiore, where he will rest with seven other popes. The Vatican on Thursday released a photo of his tomb, which Francis specified in his will should be plain. It bears only the name “Franciscus” and a reproduction of his pectoral cross.

Cardinal Rolandas Makrickas, co-Archpriest of the basilica, told reporters Francis had wanted to be buried in a tomb made from the “stone of Liguria, the land of his grandparents.” Francis was born in Argentina, but his parents were of Italian heritage.

The Vatican said on Friday that Santa Maria Maggiore would be open again to the faithful on Sunday morning but closed in the afternoon so that cardinals could visit the tomb and recite vespers, an evening prayer.

“I wish my last earthly journey to end at this very ancient Marian shrine,” Francis wrote in his will, which the Vatican released on Monday and was dated June 29, 2022. He asked to be buried “in the earth,” in a simple, undecorated tomb with only the inscription “Franciscus.”

He asked that his tomb be placed in the aisle next to the Pauline Chapel of the basilica, where an important Marian icon, the Salus Populi Romani, is. Francis was particularly devoted to the icon. In 2020, in the early days of the coronavirus pandemic, as millions died and many more lived in fear, he had the icon brought to St. Peter’s Square in the Vatican City during a moving and dramatic moment of prayer.

The mood is somber. Light applause can be heard amid a pealing church bell. A woman wipes a tear from her cheek. A man next to her makes the sign of the cross and sighs.

On Saturday, the vehicle carrying Pope Francis’ coffin will detour in the direction of the Papal Basilica of Santa Maria Maggiore, where Francis wanted to be buried. The Vatican said on Saturday that the car was a converted popemobile that had been used in a previous trip.

People lined the streets along the way. The route passes the Chiesa del Gesu, the mother church of the Society of Jesus, the religious order to which Francis belonged. It also passes the Colosseum, the 2,000-year-old Roman arena where a 17th-century fresco that was restored three years ago showed that it had also been a sacred site for Christian worship.

At Santa Maria Maggiore, a group of “poor and needy” people will be waiting on the steps, the Vatican said this week. That was fitting, the Vatican added, because St. Francis of Assisi renounced his wealth to live in poverty, and the pope “had chosen the name Francis to never forget them.”

To date, 80 of the 266 popes to serve over nearly 2,000 years have been canonized. Another 11 are on a waiting list of sorts, having been beatified, the penultimate step to sainthood.

Getting there involves years of investigation and review by the church, particularly the Dicastery for the Causes of Saints. Vatican officials and consultants examine candidates’ goodness, holiness and devotion to God and carefully scrutinizes their writings. Those who pass muster are declared “venerable.”

The next step is beatification, which requires the dicastery to accept the validity of a miracle brought about by the intercession of the candidate. After that, the Vatican must accept the validity of a second miracle attributed to the person’s intercession for them to be declared a saint. The pope makes the final decision on canonization.

The most recent pope to be canonized was Paul VI in 2018. Four years earlier, John XXIII and John Paul II became saints at a joint ceremony.

For most of the church’s history, decades usually passed between a person’s death and the beginning of a push for their canonization.

From 1588 to 1978, the average time span between a person’s death and sainthood was 262 years, according to Rachel McCleary, a researcher at Harvard University. That dropped to just over 100 years during the last three papacies, in part because John Paul II shortened the waiting period to begin a cause for sainthood, as the process is known, to five years after a person’s death.

Even that can be waived. At John Paul II’s 2005 funeral, which hundreds of thousands attended, banners and cheers rose from the mourners saying, “Santo, subito,” or “Sainthood now.” His successor, Benedict XVI, waived the waiting period, allowing John Paul to be canonized nine years after his death.

After a Vatican report in 2020 found that John Paul may have ignored accusations of sexual abuse against the disgraced former prelate Theodore E. McCarrick, critics wondered whether the pontiff been had been made a saint too soon.