Donald Trump has signed sweeping executive orders on his return to the US presidency, vowing swift action on some of his top campaign issues.

Among the directives that have gained the most publicity are an immigration crackdown and rollbacks of some climate-friendly policies.

But even presidential powers have their limits – and in some cases, he faces hurdles before his plans can become reality.

Here are six of Trump’s eye-catching actions with analysis by BBC reporters, who give their verdict on whether each order could take effect.

By Bernd Debusmann Jr, at the White House

What does the order say?

The order argues that cartels have “engaged in a campaign of violence and terror” throughout the hemisphere, and flooded the US with crime, posing a national security risk to the US.

Additionally, the order specifies that the US policy is to “ensure the total elimination” of these groups in the US. It gives US agencies 14 days to provide recommendations on which groups are to be designated and be ready to expedite the removal of individuals from the US.

What are the roadblocks?

Designating a cartel as a terrorist group could open the door to prosecuting US citizens or even legitimate businesses found to be somehow tied to those groups. The designation could also strain relations with countries including Mexico, which has vocally called for its sovereignty to be respected.

What is the potential impact?

For one, the designation of these groups as foreign terrorist organisations could ultimately be used to justify military action against targets in Mexico or other countries in which similar groups operate.

The designation could also see the US federal government dedicate more resources and enhanced legal tools to fight cartels and other gangs, and go after their business and financial interests on both sides of the border.

While it would make “material support” of these groups a crime, it remains unclear what that could mean. In theory, that could mean that drug dealers and users, including US citizens, could be charged with aiding terrorists – as could US citizens or businesses on the border that are extorted to pay them.

By Nadine Yousif, Toronto

What does the order say?

The executive order asks the US ambassador to the UN to “immediately” submit a formal written request to withdraw from the Paris climate agreement.

It says the accord does not reflect the country’s values or its economic and environmental objectives.

What are the roadblocks?

Any country can withdraw from the global climate pact, but UN regulations mean the process of removing a country can be drawn out.

Trump announced his intent to withdraw during his last term in 2017, but it was not formally finalised until 2020. We can expect another waiting period this time of at least one year.

President Joe Biden rejoined it shortly after taking office in 2021

What is the potential impact?

The US is responsible for around 11% of global greenhouse gas emissions, making it the second biggest polluter behind China. This damages the global effort to limit emissions.

Its withdrawal in the past has raised issues of trust on climate leadership, and questions about whether the agreement itself has been effective.

The withdrawal is also in line with Trump’s goal to boost domestic oil and gas production, though the US is already the number one producer of both in the world. It is one of several of Trump’s reversals of environmental protections that were enacted by the Biden administration.

By Jake Horton, BBC Verify

What does the order say?

This order aims to end birthright citizenship for children born in the US to immigrant parents who are in the country illegally, as well as those born to parents who are in the country on a temporary basis.

There have been reports that the administration will enforce the order by withholding documents, such as passports, from people it deems ineligible for citizenship.

What are the roadblocks?

The principle of birthright citizenship is established in the US Constitution. The 14th Amendment says that “all persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States”.

Courts have supported that interpretation over the past 150 years, but the Trump administration says it should not apply universally to everyone born in the US.

The legal challenges are already under way – one claims the order is “unconstitutional, and flouts fundamental American values”.

“Ultimately this will be decided by the courts. This is not something [Trump] can decide on his own,” Saikrishna Prakash, a constitutional expert, told the BBC.

What is the potential impact?

Trump has threatened mass deportations, which could include those whose birthright citizenship is revoked if Trump is successful in enforcing this executive action.

Legal cases could ultimately have to be decided by the US Supreme Court, which could take a long time.

By Dominic Hughes, health correspondent

What does the order say?

The order says the US was withdrawing “due to the organization’s mishandling of the Covid-19 pandemic”.

Trump’s longheld antipathy towards the WHO is rooted in a perception that it was dominated by – and so soft on – China, which the president has long believed was responsible for the spread of the virus.

It also mentions “unfairly onerous payments” the US made to the WHO.

What are the roadblocks?

It is the second time Trump has ordered the US be pulled out of the WHO. He began the process and Biden later reversed the decision after taking office.

The US exit won’t take effect until 2026 at the earliest, but leaving will require the approval of Congress.

On paper, the Republicans have a majority in both houses of Congress. But their numerical advantage is slim, and it would only take a few Republican defectors to potentially block the move.

What is the potential impact?

“Catastrophic”, “disastrous”, “damaging” is how some global public health experts are describing it.

Of the 196 member states, the US is by far the largest individual funder, contributing almost a fifth of the total WHO budget.

It’s possible that funding could disappear almost overnight and that could have an impact on the ability of the WHO to respond to emergencies.

There is also concern among some scientists that this would leave the US isolated when it comes to access to programmes such as pandemic preparedness and seasonal influenza strain sequencing, which is used to develop annual flu jabs.

That could ultimately harm the health of Americans, and the US national interest.

Some argue US withdrawal could prompt further reforms of how the WHO works, making it a body that better serves the public health needs of people around the globe.

By Jake Horton, BBC Verify

What does the order say?

The order calls for the Gulf of Mexico to “officially be renamed the Gulf of America”.

Trump can change the name of the Gulf on official US government documents.

This has happened on some documents already – including a weather update from Florida’s Republican Governor Ron DeSantis, which refers to “an area of low pressure moving across the Gulf of America”.

What are the roadblocks?

Trump can’t force other countries or companies to change the name.

For example, it’s currently still labelled as the Gulf of Mexico on Google Maps.

What is the potential impact?

There’s no formal international agreement for the naming of maritime areas – although there is a body that seeks to resolve disputes if raised.

So Mexico could raise an official dispute, and allies of the US and Mexico could be caught up in a diplomatic spat between the two countries.

In response to the order, Mexico’s President Claudia Sheinbaum said the US can call it the “Gulf of America”, but this won’t change what Mexico and the rest of the world call it.

By Ben Chu and Lucy Gilder, BBC Verify

What does the order say?

“It is the policy of the United States to recognize two sexes, male and female. These sexes are not changeable and are grounded in fundamental and incontrovertible reality,” it says, adding that the federal government will use the term sex, not gender identity.

President Trump’s team argues that requirements to refer to transgender people in government facilities and workplaces by pronouns that match their gender identity violates the US Constitution’s First Amendment on freedom of speech and religion.

States like Kansas and Montana have already legislated to enshrine a biological definition of sex into law.

What are the roadblocks?

There are likely to be legal challenges.

The Human Rights Campaign, which represents LGBTQ+ people, stated that “we will fight back against these harmful provisions with everything we’ve got”.

These challenges could work their way up to the US Supreme Court which, with its conservative majority, could rule in Trump’s favour.

What is the potential impact?

Prisons and settings such as shelters for migrants and rape victims would be segregated by sex under the plans, which campaigners say will help safeguard women. But transgender rights groups say trans women could be put at a heightened risk of violence.

Official identification documents, including passports and visas, would have to state whether the individual was “male” or female”. US citizens would no longer be able to select “X” as a third option.