WASHINGTON — President Trump has now been indicted for the third time, with the former president being charged Tuesday in Washington over his efforts to overturn his defeat in the 2020 election.

The federal investigation is the latest criminal case for Mr. Trump as he runs for the White House in 2024.

Special Counsel Jack Smith, who indicted Mr. Trump in the election case, has also charged Mr. Trump in federal court with the illegal retention of top secret documents. In New York, Mr. Trump faces criminal charges in a hush money case and a civil trial over his business practices. In Georgia, a county district attorney is expected to announce charging decisions in August over efforts by Mr. Trump and his allies to overturn his 2020 election loss in the state.

Mr. Trump, a Republican, has denied any wrongdoing and says he is being targeted by Democrats trying to keep him from reclaiming the presidency.

Here’s a look at some of the other top probes against the former president:

CLASSIFIED DOCUMENTS CASE

Mr. Trump has been charged by Mr. Smith in a federal case in Florida related to the mishandling of classified documents, including sensitive documents on nuclear capabilities. The 40 felony counts against him include charges of retaining classified information, obstructing justice, and making false statements.

That historic indictment — the first federal case against a former president — alleges that Mr. Trump repeatedly enlisted aides and lawyers to help him hide records demanded by investigators and cavalierly showed off a Pentagon “plan of attack” and classified map.

The top charges carry a penalty of up to 20 years in prison.

A valet for Mr. Trump, Walt Nauta, and the property manager at Mr. Trump’s Florida estate, Carlos De Oliveira, have been charged with scheming to conceal surveillance footage from federal investigators and lying about it.

Messrs. Trump and Nauta have pleaded not guilty. Mr. De Oliveira, who was charged in a superseding indictment with Mr. Trump, made an initial court appearance Monday.

A federal judge has set a trial date of May 20. If that date holds, it will mean a possible trial will not start until deep into the presidential nominating calendar and probably well after the Republican nominee is clear — though before that person is officially nominated at the Republican National Convention.

HUSH MONEY SCHEME

Mr. Trump became the first former U.S. president in history to face criminal charges when he was indicted in New York in March on state charges stemming from hush money payments made during the 2016 presidential campaign to bury allegations of extramarital sexual encounters.

He pleaded not guilty to 34 felony counts of falsifying business records. Each count is punishable by up to four years in prison, though it’s not clear if a judge would impose any prison time if Mr. Trump were convicted.

The counts are linked to a series of checks that were written to his lawyer, Michael Cohen, to reimburse him for his role in paying off a porn actor, Stormy Daniels, who alleged a sexual encounter with Mr. Trump in 2006, not long after Melania Trump gave birth to their son, Barron. Those payments were recorded in various internal company documents as being for a legal retainer that prosecutors say didn’t exist.

The former president is next set to appear in state court on December 4, two months before Republicans begin their nominating process in earnest.

GEORGIA

For over two years, the Fulton County district attorney, Fani Willis, has been investigating whether Mr. Trump and his allies illegally meddled in the 2020 election in Georgia.

She has signaled that any indictments in the case will likely come this month.

The Democratic district attorney’s investigation began shortly after the release of a recording of a January 2, 2021, phone call between Mr. Trump and Georgia’s secretary of state, Brad Raffensperger, in which the then-president suggested that Mr. Raffensperger could “find 11,780 votes” — just enough to overtake Democrat Joe Biden and overturn Mr. Trump’s narrow loss in the state.

Yet the investigation’s scope broadened considerably after that, and Ms. Willis convened a special grand jury to hear testimony from witnesses including high-profile Trump allies, such as Mayor Giuliani and Senator Graham of South Carolina, and high-ranking Georgia officials, such as Mr. Raffensperger and Governor Kemp.

Prosecutors advised Mr. Giuliani and Georgia Republicans who served as fake electors that they were at risk of being indicted. The fake electors signed a certificate asserting Mr. Trump had won the election and declaring themselves the state’s rightful electors, even though Mr. Biden had won the state and Democratic electors had already been certified.

A court filing in early May indicated that Ms. Willis had reached immunity deals with at least eight fake electors, suggesting they may be cooperating with authorities.

The foreman on the special grand jury indicated publicly that the panel had recommended multiple indictments. Ms. Willis is expected to ask a regular grand jury to return indictments in the case.

Mr. Trump has described his phone call to Raffensperger as “perfect.”

NEW YORK CIVIL CASES

New York’s attorney general, Letitia James, has sued Mr. Trump and the Trump Organization, alleging they misled banks and tax authorities about the value of assets including golf courses and skyscrapers to get loans and tax benefits.

That lawsuit could lead to civil penalties against the company if Ms. James, a Democrat, prevails. She is seeking a $250 million fine and a ban on Mr. Trump doing business in New York. Manhattan prosecutors investigated the same alleged conduct but did not pursue criminal charges.

A civil trial is scheduled in state court for October.

In a separate civil case in federal court in New York, Mr. Trump was found liable in May of sexually abusing and defaming a former magazine columnist, E. Jean Carroll, in the mid-1990s. The jury rejected Ms. Carroll’s claim that Mr. Trump had raped her in a dressing room.

Mr. Trump was ordered to pay $5 million to Ms. Carroll. He has appealed and has adamantly denied her accusations. In July, a federal judge upheld the jury’s verdict against Mr. Trump, rejecting the former president’s claims that the award was excessive.