In recent days, iPhone apps have been changing. The Kindle app now lets people buy books directly from its site. Spotify is offering users free trials. And Patreon, a subscription service, is letting people pay creators more money.

The changes are an early look at how a recent court ruling could transform the shopping experience on an iPhone. Last week, a federal judge ordered Apple to start allowing apps to offer promotions and collect payments directly from users. The decision makes it possible for apps to offer people new conveniences, like buying books directly from their website. The ruling also lets apps bypass a 30 percent commission that Apple collects on every app sale, which could lead to lower prices for consumers.

For more than a decade, Apple required that apps use its payment system for purchases and collected commission on the sales.

Now, all of that is open to change. Here’s what could be different in the future and why.

What did the judge rule?

Judge Yvonne Gonzalez Rogers, who began working on this case after Epic Games sued Apple in 2020, ruled that Apple could no longer take commissions from sales that link out from the app. She also restricted the company from writing rules that would prevent developers from creating buttons or links allowing people to pay apps directly for their goods and services, and said it could not create messages — known as warning screens — that discourage users from leaving the App Store.

How will iPhone apps change?

For years, Kindle has not sold books on its app to avoid Apple’s 30 percent commission. Now, it has added a “Get Book” button that directs users to its website to buy books. Similarly, Apple prevented Spotify from offering free trials to new customers, but now Spotify has a button on its app for a three-month trial.

Other apps could begin offering links for buying directly from stores online, which would allow the business to avoid having to pay Apple’s 30 percent commission. Without having to pay those fees, apps could offer users lower prices, reducing a $10 monthly subscription to $7.

What will this cost Apple?

Apple makes $11 billion a year from app sales in the United States, according to estimates by Morgan Stanley. It won’t lose all of that, but the bank estimates that $2 billion of that is now at risk.

How much Apple loses will come down to how willing people are to change their behavior. The decade-old process for buying software and services on apps is not only familiar but also quick. People trust Apple with their credit card information. And the company makes it easy for people to cancel their subscriptions — keeping them all in one place. Many people may be reluctant to leave the App Store to make their purchases, and apps may prefer to maintain the current system.

What does this mean for the rest of the world?

Now that Apple is required to allow apps to collect payment directly, without paying the company a commission, in the United States, other countries are going to press for similar concessions. Regulators in Europe, Japan and South Korea, which have been asking Apple to loosen its grip on the App Store, would not want their own citizens or developers to have to pay more than Americans did.

Could Apple roll back the changes?

Apple said it planned to appeal the ruling, but it would be challenging for the company to have the decision overturned. In 2021, the judge wrote a less prescriptive ruling. Apple skirted the rule by introducing a 27 percent commission for app sales. The U.S. Court of Appeals for the Ninth Circuit sided with the judge’s initial ruling from 2021 and is unlikely to change its position, said Mark A. Lemley, a professor of antitrust and technology law at Stanford. “They should take their licks and let it be,” he said.

The last several months for American Catholics have been a story about the ascent of the Catholic right. In January, a parade of right-wing Catholic power began streaming into President Trump’s remade Washington. Just weeks later came the hospitalization and decline of Pope Francis, who often seemed to stand alone in offering a different vision of global Christian influence.

Vice President JD Vance, a Catholic in the new conservative style, was one of the last people to see Pope Francis alive, a brief meeting between representatives of two contrasting visions for Catholic values in the world.

Then came the stunning arrival on Thursday of a new pope: an American, Chicago-born — and a prelate whose priorities for the church seemed to place him in the mold of Francis. He is potentially another countervailing voice against the country’s newly powerful strain of right-leaning Catholics.

The elevation of Robert Francis Prevost, known to some as Bob, to the throne of St. Peter electrified Catholics across his home country on Thursday afternoon. But the first American pope arrives at a time of extraordinary complexity and tension in the church in the United States.

Now the new pope, Leo XIV, faces the task not just of shepherding the world’s 1.4 billion Catholics, but of unifying a fractured American church where the church hierarchy, ordinary Catholics, an influential right-wing Catholic media ecosystem and Catholic power in Washington are often at odds.

The pope assumes the role at a moment of extraordinary muscle and visibility for a certain kind of Catholicism in American public life. More than a third of the members of President Trump’s cabinet are Catholic. So are two-thirds of the Supreme Court, which has issued a remarkable run of rulings expressing an emphatic vision of religious liberty, often favorable to Christian interests.

The second Catholic president in the nation’s history, Joseph R. Biden Jr., left office just months ago.

The rise of a new right-wing Catholicism in Mr. Trump’s Washington contrasts with a broader decline of the presence of the church in American life. Waves of Catholics left the church following revelations of widespread sexual abuse by clergy, and American culture overall has become more secular. Today, about 20 percent of Americans describe themselves as Catholic, a share that has remained stable over the past decade, according to the Pew Research Center.

Mr. Vance, who converted to the faith in 2019, posted his well-wishes to the new pontiff online on Thursday afternoon. “Congratulations to Leo XIV, the first American Pope, on his election!” he wrote. “I’m sure millions of American Catholics and other Christians will pray for his successful work leading the Church. May God bless him!”

Mr. Trump, who denied posting an image of himself as the pope on his own account on his own Truth Social platform this week, told reporters on Thursday that the selection was “such an honor for our country.”

Pope Francis clashed with Mr. Trump, most recently and fervently over immigration. In February, just months before he died, the pope harshly criticized Mr. Trump’s policy of mass deportations in an open letter to American bishops, calling it a violation of the “dignity of many men and women, and of entire families.” The letter was also seen as an indirect message to other members of the administration, including Mr. Vance, who used a Catholic theological concept to defend the administration’s crackdown on immigrants.

Pope Leo is seen as likely to share Pope Francis’ priorities on a range of social issues. An X account that appeared to belong to the new pope reposted a message in April critical of the Trump administration’s “illicit deportation” of Kilmar Abrego Garcia, the man mistakenly deported to El Salvador in March. The same account has also shared several articles critical of Mr. Vance.

“This pope is clearly going to keep speaking out of for justice, for peace, refugees, the poor and the hungry,” the Rev. Thomas J. Reese, a longtime Vatican analyst, said. “If this gets him in trouble with the Trump White House, so be it.”

On Thursday night, some right-wing Catholic media outlets were beginning to express skepticism of Pope Leo’s orthodoxy. The website LifeSiteNews published “5 worrying things you need to know about Leo XIV,” written by its editor in chief. The list included the new pope’s criticisms of Mr. Trump’s immigration policies.

Still, Catholic doctrine does not map neatly onto American political disputes, and it’s not clear whether Pope Leo will have his predecessor’s appetite for sparring. Inserting himself directly into the American political landscape could be thornier for an American.

For some American Catholics, his selection was a sign that the church here is entering maturity. The country is approaching its 250th birthday next year, but the Catholic Church claims an age about 1,750 years older.

The United States was still considered mission territory for the Catholic Church as recently as the beginning of the 20th century, said Kim Daniels, director of the Initiative on Catholic Social Thought and Public Life at Georgetown University. “A pope from the U.S. is in some ways a sign of our coming into our own in global Catholicism,” she wrote in an email, calling his election “an extraordinary gift” to the life of the American church.

The American church is now the fourth largest in the world, behind those in Brazil, Mexico and the Philippines. The U.S. is the first among them to birth a pope.

For leaders of Catholic institutions and ministries across the country, the selection was a moment of optimism for their church and their country.

“It’s wonderful news, it’s amazing,” said Curtis Martin, founder of the American-based Catholic ministry FOCUS, about the selection of an American pope. The name feels auspicious to him, too: Mr. Martin named one of his sons after the turn-of-the-century Pope Leo XIII, who was born in Italy.

Mr. Martin said he saw Pope Francis as a leader who excelled at listening, especially to those who did not understand the church or agree with its teachings. He hopes Pope Leo will be able to take the next step, listening but also speaking more directly about church teachings.

“What hasn’t happened yet is the opportunity to enter into a real dialogue,” Mr. Martin said. “The church has maybe never listened better than it did under Pope Francis, but now it’s an opportunity to speak.”

He added, “I think Pope Leo might be able to lead that.”

The Rev. Robert A. Dowd, the president of the University of Notre Dame, said that he hoped that Leo’s election could prove “a uniting moment” for the American church.

“He’s an American with a global perspective, but he’s an American,” Father Dowd said. “He understands, I think, the state of the church here in the United States.”

As significant as the moment felt to many American Catholics, the new American pope has spent much of his adult life overseas, in Peru and Italy. Pope Francis, who was born in Argentina, never returned to his own home country as pope, and he visited the United States only once in his 12-year papacy.

Leaders of the American church, who are generally more conservative than much of the global church, expressed their welcome and emphasized that the new pope now belongs to the world.

“Certainly, we rejoice that a son of this nation has been chosen by the cardinals, but we recognize that he now belongs to all Catholics and to all people of good will,” Archbishop Timothy P. Broglio, president of the United States Conference of Catholic Bishops, said in a statement. “His words advocating peace, unity, and missionary activity already indicate a path forward.”

Alan Blinder contributed reporting.

For the past three weeks, the Justice Department and Google have questioned more than two dozen witnesses to try to sway a federal judge’s decision over how to address the company’s illegal monopoly in internet search.

On Friday, that hearing in the U.S. District Court for the District of Columbia is expected to conclude. To fix the monopoly, the government has proposed aggressive measures that include forcing Google to sell its popular Chrome web browser and share proprietary data with competitors. Google has argued that small tweaks to its business practices would be more appropriate.

Both sides will offer closing arguments at the end of the month. Judge Amit P. Mehta, who is presiding over the case, is expected to reach a decision by August. His ruling could have significant implications for Google, its rivals and the way that people look for information online.

Here’s what to know about what was argued at the hearing.

What case does the hearing stem from?

In August, Judge Mehta ruled that Google had broken antitrust law when it paid companies like Apple, Samsung and Mozilla billions of dollars to automatically appear as the search engine in browsers and on smartphones. He also ruled that Google’s monopoly allowed it to inflate the prices for some search ads, adding to its unfair advantage.

Judge Mehta convened the hearing last month to determine how to best address the search monopoly through measures called remedies. Executives from Google, rival search engines and artificial intelligence companies — alongside experts — testified about Google’s power over the internet.

What did the government argue?

The only way to end Google’s dominance in search is by taking significant action, government lawyers said at the hearing.

Lawyers argued that Google should be forced to spin off Chrome and share search results and ads with rivals, allowing them to populate their own search engines. Other search engines and some artificial intelligence companies should get access to data on what Google users search for, as well as the websites they click on.

The government warned during the hearing that if Judge Mehta didn’t take action, it could propel Google into dominance of another technology, artificial intelligence. Search is in upheaval as A.I. and chatbots, like Google’s Gemini, change the way people find information on the web.

“This court’s remedy should be forward looking and not ignore what’s on the horizon,” said David Dahlquist, the government’s lead litigator. “Google is using the same strategy that they did for search and now applying it to Gemini.”

Eddy Cue, an Apple executive called as a witness by Google, said that “in the past two months for the first time in over 20 years,” Google search queries had declined in the company’s Safari browser for the first time. He attributed the drop to the growth of A.I.

What did Google argue?

Google’s lawyers said the government’s proposal would endanger products that consumers love and imperil privacy and security for internet browsing.

“I think it definitely will have many unintended consequences,” testified Sundar Pichai, Google’s chief executive.

Sharing Google’s data with its competitors would undermine the privacy of its users, the company’s lawyers said. They pointed multiple times to a 2006 incident in which AOL released search data to aid academic researchers. Journalists were able to use leaked data to identify an individual based on her searches.

There’s also plenty of competition in A.I., they said, noting the success of OpenAI’s ChatGPT and other examples.

Google’s lawyers instead proposed that its contracts with web browsers and smartphone companies should offer more freedom to work with competing search and A.I. services. Mr. Pichai testified that Google had already started altering its contracts with other companies to align with its proposal in the case.

(The New York Times has sued OpenAI and its partner, Microsoft, for copyright infringement of news content related to A.I. systems. They have denied wrongdoing.)

What did other companies say?

During the hearing, several Google competitors, including OpenAI and the chatbot company Perplexity, said they would be open to buying Chrome if it was put up for sale. Government witnesses said access to Google’s search and ad data would give A.I. companies an advantage as they tried to compete with Google.

What did the judge say?

When Judge Mehta questioned witnesses throughout the hearing, he provided a window into his thinking.

At times, he pushed witnesses to say whether any rivals could compete with Google’s search dominance absent the court’s intervention.

Many of his questions revolved around A.I. and its significance, as Google battles its rivals to develop the technology that has become a major force in the tech industry.

When Mr. Pichai was on the witness stand, Judge Mehta said he had observed the rapid development of A.I. since the lawsuit went to trial in the fall of 2023, signaling he was aware of how the growth of the technology had become the backdrop for the hearing.

“One of the things that has struck me, Mr. Pichai, about these proceedings is, when we were together not so long ago, the consistent testimony from the witnesses was that the integration of A.I. and search or the impact of A.I. on search was years away,” he said, referring to testimony during the 2023 trial. “By the time we’ve gotten here today, things have changed dramatically.”