Here are the lawyers arguing before the Supreme Court.

The two lawyers arguing before the Supreme Court on Thursday have each played a role in some of the defining legal battles stemming from Mr. Trump’s term in office.

Arguing the case for the special counsel Jack Smith will be Michael Dreeben, who worked for a different special counsel’s office that scrutinized Mr. Trump’s presidency: Robert S. Mueller III’s investigation into links between Russia and associates of Mr. Trump. Mr. Dreeben, one of the nation’s leading criminal law experts, has made more than 100 oral arguments before the Supreme Court, including when he served as deputy solicitor general.

On Mr. Mueller’s team, he handled pretrial litigation, defending the scope of the investigation and preventing the office from losing cases on appeal. He also helped with a second part of Mr. Mueller’s investigation, examining whether Mr. Trump had tried to obstruct the inquiry in his dealings with associates involved in the case.

Mr. Dreeben, who was heavily involved in the writing of Mr. Mueller’s final report on his investigation, supported an interpretation of presidential power that emphasized limits on what a president could do while exercising his or her powers, according to “Where Law Ends,” a book written by Andrew Weissmann, another prosecutor on Mr. Mueller’s team.

After Mr. Mueller’s investigation concluded, Mr. Dreeben took a teaching position at Georgetown University’s law school and returned to private practice at O’Melveny, arguing in front of the Supreme Court on behalf of the city of Austin over a First Amendment dispute about the placement of digital billboards.

Opposing Mr. Dreeben in front of the Supreme Court will be D. John Sauer, a lawyer based in St. Louis who once served as the solicitor general of Missouri. Mr. Sauer joined Mr. Trump’s legal team late last year to handle appellate matters, including his challenge to a gag order imposed on him in the election case in Washington.

As Missouri’s solicitor general, Mr. Sauer took part in a last-ditch effort to keep Mr. Trump in power after his defeat in the 2020 election, filing a motion on behalf of his state and five others in support of an attempt by Texas to have the Supreme Court toss out the results of the vote count in several key swing states.

He also joined in an unsuccessful bid with Texas in asking the Supreme Court to stop the Biden administration from rescinding a Trump-era immigration program that forces certain asylum seekers arriving at the southwestern border to await approval in Mexico.

When he left the solicitor general’s office last January, Mr. Sauer, who once clerked for Justice Antonin Scalia, returned to his private firm, the James Otis Law Group. The firm is named after a prominent Revolutionary War-era lawyer who built a career out of challenging abuses by British colonial forces.