Washington (AFP) - Donald Trump on Tuesday became the first US president to be arrested on criminal charges -- but the 34 felony counts for allegedly falsifying business records are far from the only legal peril threatening the ex-leader as he seeks a return to the White House.

The rebellious Republican billionaire has described the charges as being the work of "radical left Democrats" who have "criminalized the justice system" and are seeking to derail his presidential candidacy.

Here are other key investigations underway against the 76-year-old one-term president:

- Incited Capitol attack? -

An independent federal prosecutor, Jack Smith, will decide whether or not to charge anyone alleged to have "unlawfully interfered with the transfer of power" after the 2020 election or during certification by Congress of the results.

On January 6, 2021, a mob of Trump supporters stormed the US Capitol seeking to stop that certification.

Just before the assault, Trump delivered a fiery speech nearby urging the crowd to "fight like hell."

In explosive hearings separate from the Department of Justice probe, lawmakers argued Trump knew he lost the election yet pressed fake claims of fraud.

They also presented evidence of alleged misconduct by Trump leading up to the insurrection, including accusations he attempted to co-opt government agencies into his bid to overturn the election results.

Federal prosecutors have obtained convictions of or guilty pleas from more than 500 people for participating in the uprising, but it remains unclear if Trump will face charges for any plotting or fomenting of the Capitol attack.

Keeping classified docs at home

Smith will also decide on any charges in the ongoing investigation into classified documents found at Trump's Florida home -- and over possible obstruction of the probe.

An FBI search of Trump's palatial Mar-a-Lago residence last August turned up classified documents taken when he left office in early 2021.

The raid was triggered by a review of records which Trump finally surrendered to authorities in January 2022.

The Justice Department began investigating after the 15 boxes were found to contain national defense information, including 184 documents marked as confidential, secret or top secret.

Georgia election meddling, and more

Trump is separately being investigated for pressuring officials in the southern swing state of Georgia to overturn Biden's 2020 victory -- including a taped phone call in which he asked a state official to "find" enough votes to reverse the result.

The top prosecutor in Georgia's Fulton County, Fani Willis, has assembled a special grand jury that could see Trump facing conspiracy charges connected to election fraud and interference.

Last month the grand jury forewoman, in unusually public remarks, said the 23-member panel had recommended indictments of multiple people, including "certainly names that you would recognize." She did not say whether Trump was among them.

In New York, meanwhile, the state attorney general Letitia James has filed a civil suit against Trump and three of his children, accusing them of fraud by overvaluing assets to secure loans and then undervaluing them to minimize taxes.

James is seeking $250 million in penalties as well as banning Trump and his children from serving as executives at companies in New York.