Here’s the latest.

On Tuesday, Mr. Musk took the stand to lay out the claims in his 2024 lawsuit. He argued that OpenAI took advantage of his donations and breached its founding agreement by putting commercial interests first. Mr. Musk framed the case as fundamental to “the entire foundation of charitable giving in America,” accusing his co-founders of stealing from the public good.

Mr. Musk is seeking more than $150 billion in damages from OpenAI and Microsoft, OpenAI’s biggest financial partner. He is also asking the court to remove OpenAI’s co-founder and chief executive, Sam Altman, from the board, and to stop its recent shift to operate as a for-profit company.

OpenAI’s lead counsel, William Savitt, argued on Tuesday that Mr. Musk filed the lawsuit because the world’s richest person “didn’t get his way at OpenAI.” The start-up’s original nonprofit continues to oversee the for-profit company, and is working to redistribute billions of dollars generated by the commercial operation, he added.

The trial’s outcome could upend the A.I. landscape. OpenAI is a leading A.I. company. A win for Mr. Musk would also be a win for OpenAI’s competitors, from industry giants like Google to young companies like Anthropic and Mr. Musk’s own A.I. lab, xAI.

A loss for Mr. Musk would mean that OpenAI, which is now valued at about $730 billion, will be free to continue its commercial course just as it appears to be heading toward one of the biggest initial public offerings in history.

(The New York Times has sued OpenAI and Microsoft, claiming copyright infringement of news content related to A.I. systems. The two companies have denied the suit’s claims.)

Here’s what to know:

• High-profile witnesses: Mr. Altman and several other key industry figures, including Microsoft’s chief executive, Satya Nadella, and Mira Murati, OpenAI’s former chief technology officer, are slated to testify later in the trial.

• Trial logistics: The trial is expected to take about four weeks before a nine-person jury at the federal courthouse in Oakland, Calif. If the jury rules in Mr. Musk’s favor, Judge Yvonne Gonzalez Rogers, who also oversaw a high-profile lawsuit against Apple over its control of the App Store, will decide on monetary damages and other remedies.

• Musk’s social media: Judge Gonzalez Rogers on Tuesday called Mr. Musk, who assailed Mr. Altman on X before the trial, to the bench to discuss whether there should be a gag order preventing him from posting on social media about the trial. “How can we get things done without you making things worse outside the courtroom?” she asked. The judge asked him and Mr. Altman to start with a “clean slate” and “keep things to a minimum” on social media. They all agreed, and Mr. Musk has thus far complied.

Mr. Musk sued OpenAI in 2024 over claims that OpenAI took advantage of his financial resources and breached its founding agreement by putting commercial interests over the public’s.

Mr. Musk’s claims do not stem from a moral high ground, OpenAI’s lead counsel, William Savitt, argued. Instead, it was “sour grapes” over the commercial success of the A.I. start-up after its release of ChatGPT in 2022, Mr. Savitt said.

Mr. Musk “didn’t understand artificial intelligence very well,” Mr. Savitt added.

Mr. Musk took issue only with OpenAI’s for-profit pursuits after ChatGPT set a global A.I. arms race into motion, Mr. Savitt said, and Mr. Musk started his own for-profit A.I. company, xAI.

“My clients had the nerve to go on and succeed without him. Mr. Musk did not like that,” Mr. Savitt said.

Mr. Savitt showed the jury emails from before Mr. Musk’s departure in which his chiefs of staff discussed ways to establish a for-profit OpenAI operation. In those emails, the chiefs floated giving Mr. Musk a 55 percent stake in the for-profit effort, while giving Mr. Altman a 7.5 percent stake.

Mr. Savitt also explained OpenAI’s byzantine structure at length, telling the jury that, despite Mr. Musk’s claims, the company had not abandoned its nonprofit mission. Its nonprofit foundation “remains in control of the organization” and was “doing leading edge work to cure diseases and promote economic diversity,” he said.

On the witness stand at the trial, Mr. Musk also underscored his savior credentials. He said that his rocket maker, SpaceX, was dedicated to the survival of the human race. The company was “life insurance for life as we know it.” And he positioned himself as a bulwark against dangerous A.I. that “could kill us all.”

Mr. Musk has long positioned himself as a savior. He has said that he founded SpaceX in 2002 to take humans to Mars and to make life multiplanetary in case of a catastrophic event on Earth. He bought Twitter, now X, for $44 billion in 2022 not to make more money, he said, but to “help humanity.” And he has said he supported President Trump in the 2024 election to save “the fate of western civilization.”

This mission-oriented language has served Mr. Musk well in business. He has used life-or-death scenarios to motivate employees toward achieving seemingly impossible goals, former workers at SpaceX and Tesla, his electric carmaker, have told The New York Times. Such language may also help rally investors and customers who believe they are supporting Mr. Musk’s companies beyond just products or investment returns.

Mr. Musk, who is taking SpaceX public soon in a deal that could make him a trillionaire, has lofty ideals, said Peter Diamandis, the founder of the XPrize Foundation, which encourages science breakthroughs through contests, and who is also a SpaceX investor. Mr. Musk cares far more about “uplifting humanity” than money, Mr. Diamandis said.

Mr. Musk co-founded OpenAI with Mr. Altman and other artificial intelligence researchers in 2015 as a nonprofit A.I. lab. But Mr. Musk left the nonprofit in 2018 after a power struggle with Mr. Altman. After his departure, OpenAI tacked on a for-profit entity and found huge commercial success after the 2022 public launch of ChatGPT and a lucrative partnership with Microsoft.

Mr. Musk sued OpenAI in 2024, claiming in part that Mr. Altman took advantage of the donations he poured into the start-up to enrich himself.

OpenAI’s shift away from a nonprofit amounted to theft, Mr. Molo argued.

“No one should be allowed to steal a charity,” he said. “To steal a charity is absolutely wrong.”

Mr. Molo also attempted to front-run a key issue: Mr. Musk had discussed creating a for-profit version of OpenAI before his departure. But Mr. Musk’s intention was always for the nonprofit to have strict oversight over the for-profit entity, Mr. Molo argued.

“The concept was that Elon would have control over the for-profit subsidiary, but the importance of this subsidiary would be diminished over time,” Mr. Molo said, adding that Mr. Musk merely saw the move as a way to raise money in the short term.

Mr. Molo acknowledged that Mr. Altman does not have a stake in OpenAI — a fact that could undermine Mr. Musk’s claim that Mr. Altman unjustly enriched himself through the nonprofit. But Mr. Altman enriched himself through various companies that do business with OpenAI, Mr. Molo argued. Mr. Altman also has said he might take equity in OpenAI in the future, Mr. Molo added.

When Mr. Musk founded OpenAI with Mr. Altman and several young A.I. researchers, he saw the research lab as a necessary counterweight to the A.I. work underway at Google. He believed that Google and Larry Page, one of its founders, did not understand the dangers of A.I.

OpenAI’s founders — backed largely by donations from Mr. Musk — vowed to freely share their technology with the public as open source software. They argued that A.I. would be too powerful and too dangerous to be controlled by a single company.

But by late 2017, many inside OpenAI were arguing that open sourcing may be more dangerous than keeping the technology closed. And they worried that if the lab remained a nonprofit, it might not raise the money needed to reach its lofty goal of building artificial general intelligence, or A.G.I., a machine that can do anything the human brain can do.

That included Mr. Musk. In February 2018, he forwarded an email to the lab’s other founders suggesting that OpenAI attach itself to Tesla, his electric car company, and build its A.I. using the supercomputers that Tesla was developing.

“Tesla is the only path that could even hope to hold a candle to Google,” he wrote. “Even then, the probability of being a counterweight to Google is small. It just isn’t zero.”

After Mr. Altman and others refused to give Mr. Musk control, he quit. Later that month, he announced his departure to OpenAI’s staff on the top floor of the lab’s office in San Francisco. He withdrew his financial support for the lab.

Forced to find other sources of funding, Mr. Altman bolted a for-profit company onto the original nonprofit and eventually raised $13 billion from Microsoft. The lab also curtailed its efforts to open-source its technologies.

OpenAI has since emerged as one of the most important tech companies in the world, worth an estimated $730 billion as a for-profit company overseen by the original nonprofit. The start-up is heading toward one of the biggest initial public offerings in history, which could come as soon as this year.

The company has expanded to more than 4,000 employees working in offices around the world, and is pursuing a data center expansion plan that could cost hundreds of billions of dollars.