US President Donald Trump's agenda has partially stalled in court as judges block his efforts to crack down on immigration and rein in Elon Musk's hunt for government fraud and waste, though the administration has scored some wins and is appealing its losses.

Courts are tackling some 133 legal challenges to the Trump administration's actions, according to Just Security, a legal news site.

Here is a look at recent developments in some of the cases.

Judge blocks deportations

A federal judge temporarily ordered the Trump administration to halt deportations of hundreds of alleged Venezuelan gang members to a mega-prison in El Salvador.

Three deportation flights landed there after that order, but the government denied violating it, sparking an ongoing legal standoff over whether officials were defying the judge.

The administration argues the judge overseeing the case, James Boasberg, has no authority to stop the deportations under the Alien Enemies Act, a centuries-old law that gives the president power to deport people whose primary allegiance is to a foreign power and who might pose a national security risk in wartime.

Boasberg said he is skeptical the administration can apply that law to the deportations because it is intended for enemies in wartime. He has also demanded answers about the precise timings of the flights and the administration's compliance with his order, calling its responses so far "woefully insufficient."

On Monday, Boasberg denied the Trump administration's request to set aside a temporary ban imposed earlier this month on deportations.

Judges have also temporarily blocked the administration from deporting several students and academics who engaged in pro-Palestine protests on college campuses. Lawyers for the protesters say they are lawfully residing in the US and being unfairly targeted for political reasons.

DOGE blocked from 'unbridled' access to social security data

A judge on March 20 blocked Elon Musk's Department of Government Efficiency (or DOGE) from having "unbridled access" to data of millions of Americans at the Social Security Administration, saying the arrangement likely violated privacy laws.

The ruling was one of the most significant legal setbacks to date for Musk and his deputies at DOGE, whom Trump has deputized to root out waste and fraud in government.

On March 19, another judge found Musk's moves to shut down the US Agency for International Development likely violated the Constitution because he is not a Senate-confirmed cabinet official. Courts have also raised concerns about DOGE's structure and lack of transparency.

One judge has ordered the department to turn over records detailing its operations in a lawsuit challenging Musk's authority.

Judges have declined to block DOGE from accessing computer systems at the departments of Labor, Health and Human Services, Energy and others, although the team has been barred from accessing sensitive Treasury Department payment systems.

Court halts firing of federal workers

Two judges have separately ruled that the Trump administration's firings of 25,000 probationary federal workers were likely illegal and ordered them reinstated pending further litigation.

Both judges said the mass firings appeared to violate regulations that only permit the federal government to fire certain workers for individualized reasons. Agencies covered by the orders include the US Departments of Agriculture, Commerce, Education, Energy, Health and Human Services, Homeland Security, Housing and Urban Development, Interior, Labor, Transportation, Treasury and Veterans Affairs.

The Trump administration has said it is working to bring all of the employees back but has appealed both decisions. On March 21, an appeals court declined to pause one of the orders.

Rolling back DEI policies

A judge on March 10 ordered the Trump administration to temporarily restore grants for teacher preparation it nixed as part of its efforts to eradicate diversity, equity and inclusion (DEI) initiatives, finding the Department of Education provided "no reasoned explanation" for cutting the funding.

In a win for Trump, an appeals court ruled his administration could temporarily implement a ban on DEI programmes at federal agencies and businesses with government contracts, undoing a lower court order that blocked the move.

Judges block Trump's bid to nullify birthright citizenship

The Trump administration has escalated its challenge to birthright citizenship to the US Supreme Court. Several courts have blocked Trump's executive order issued on his administration's first day.

Trump's claim that birthright citizenship is unconstitutional is fringe, as the Supreme Court ruled otherwise 127 years ago, and this decision remains unchanged.