(CNN) Reagan and Thatcher. Bush and Blair. Obama and Cameron. And now? Trump and May.

The close relationship between US and British leaders dates back to Winston Churchill and Franklin D. Roosevelt, but how the long-standing "special relationship" will fare under US President Donald Trump's isolationist administration and UK Prime Minister Theresa May's Brexit Britain is still in question.

May met with Trump at the White House on Friday, becoming the first foreign leader to meet the new president. Here's a look at how each of them sees the world.

TRADE

Trump's view:

Trump campaigned on protectionist trade policies throughout his candidacy and he's spent the first few days as president signing executive orders that reinforce his vow to put "America first."

On his first day in office, he signed an executive action to withdraw from the negotiating process of the Trans-Pacific Partnership -- a deal he previously described as a "disaster done and pushed by special interests who want to rape our country." He's also said he wants to renegotiate the North American Free Trade Agreement (NAFTA), with the possibility of abandoning it all together.

Trump has expressed openness to execute a new trade deal with the UK, but has said he will prioritize American jobs.

May's view:

May is a proponent of free trade and globalization -- branding her vision of a "Global Britain" that's "open for business" in her Brexit plans.

But May's global vision might not reach as far as she hopes.

When the UK leaves the single market, which guarantees the free movement of goods, services and people within the 28 member bloc, it will need to negotiate a new trade deal with all member countries.

As the EU will give preference to its member states first, the UK might not get the deals it wants. This is one of the reasons May is keen to strike a new free trade deal with the US.

May has said she will seek free-trade agreements with individual countries in and out of Europe and will use her meeting with Trump to start preliminary talks.

"It will take detailed work, but we welcome your openness to these discussions and hope we can make progress so that the new global Britain that emerges after Brexit is even better equipped to take its place confidently in the world," she said.

But even if Trump is open to a new UK trade partnership, the UK won't be able to sign any agreements until it officially leaves the EU, a process which hasn't officially started and is likely to take at least two years.

NATO

Trump's view:

Trump has sent mixed messages on NATO. He's repeatedly called the organization obsolete and dedicated campaign air-time to rally against members of the 28-country alliance for not contributing to the recommended defense spending levels of around 2% of GDP.

Mattis, a strong supporter of NATO, spoke with Secretary General Jens Stoltenberg and three alliance partners including the UK this week and reaffirmed that the US had an "unshakeable commitment to NATO."

Mattis and Stoltenberg said they "looked forward to working together to strengthen the Alliance, including by increasing defense spending and doing even more to fight terrorism," according to a statement released by NATO.

May's view:

At the GOP gathering, May said both countries should be "proud" of their commitment to NATO -- an organization that she called "the cornerstone of the West's defense...established on the bonds of trust and mutual interests that exist between us."

In the speech, she also acknowledged Trump's suspicions of the organization -- stating that NATO, along with the UN, The World Bank and the International Monetary Fund were "in need of reform and renewal to make them relevant to our needs today." But she later stressed that "America's leadership role in NATO -- supported by Britain -- must be the central element around which the Alliance is built."

Last week, May reaffirmed her dedication to the alliance , and said that she would reiterate to Trump its importance in their meetings after speaking with Stoltenberg.

According to the British Ministry of Defence, the UK spends 2.1% of its annual GDP on NATO.

IMMIGRATION

Trump's view:

He campaigned hard on building a border wall with Mexico, creating a Muslim registry and getting tough on illegal immigration.

On Wednesday, Trump signed two executive orders on immigration and border security, which included plans to build the wall and add increased spending to immigration enforcement and deportations.

If enacted, Trump's refugee ban would last for four months. After 120 days, the US would then prioritize admissions of refugees who are fleeing religious persecution from Iraq, Syria, Iran, Sudan, Libya, Somalia or Yemen, "provided that the religion of the individual is a minority religion in the individual's country of nationality," according to the draft order obtained by CNN.

Admissions for Syrian refugees would be suspended indefinitely until the vetting process sees an overhaul. The plan would cap the total number of refugees admitted into the US during the 2017 fiscal year in half.

May's view:

In her speech to the 2015 Conservative Party Conference, May, then Home Secretary, laid out her position on immigration -- echoing the same hardline stance she's taken as Prime Minister. In it, she suggested that the anger and resentment felt by Brits out of work was spurred by immigration, she also claimed a significant number of asylum seekers were "foreign criminals" and argued immigrants made society less "cohesive."

How immigration will look under Brexit is still unclear, although the Prime Minister has said she wanted to guarantee the rights of EU citizens already in Britain and British citizens in other EU states "as early as we can."

Regarding future immigration from European countries, May said: "Brexit must mean control of the number of people who come to Britain from Europe. And that is what we will deliver."

RUSSIA

Trump's view:

Trump has referenced that he wants to see a major shift in US-Russia relations during his presidency. He recently said: " If Putin likes Donald Trump, I consider that an asset."

Trump has expressed an openness to work with Putin , and has said that Russia could be a partner in the fight against ISIS. While President-elect, he also suggested he was open to the possibility of lifting sanctions on Russia -- with the caveat that the country aids the US in its ongoing battle against terrorism. Both countries are looking to boost their nuclear capabilities, raising the prospect of a new arms race between the US and Russia.

For now, Trump said he plans to keep sanctions for "at least a period of time."

He also recently acknowledged that Russia was behind the hacking of the Democratic National Convention during the campaign -- but added they "were totally open to be hacked." Russia has repeatedly denied any involvement in the US election campaign.

May's view:

May seems more wary about opening up relations with Russia -- and suggested that Trump approaches the Kremlin with caution. "With President Putin, my advice is to engage but beware," she told top Republicans in Philadelphia.

She also stressed mutual cooperation to maintain security in the former Soviet states. "We should build the relationships, systems and processes that make co-operation more likely than conflict -- and that, particularly after the illegal annexation of Crimea, give assurance to Russia's neighboring states that their security is not in question. We should not jeopardize the freedoms that President Reagan and Mrs Thatcher brought to Eastern Europe by accepting President Putin's claim that it is now in his sphere of influence," she said.

In December, May joined other world leaders in denouncing Russia's involvement in the Syrian conflict and supports Britain's continued sanctions in response to Russia's role in "destabilizing Eastern Ukraine."

CLIMATE CHANGE

Trump's view:

Although his pick to lead the Environmental Protection Agency, Scott Pruitt does not believe climate change is a hoax, the former Oklahoma attorney general is a long time EPA skeptic and has sued the agency many times.

Trump's said that the US will "cancel" the Paris agreement , a landmark climate change agreement that commits countries to reduce their greenhouse gas emissions with the aim of keeping a rise in global temperatures to within 1.5 degrees Celsius.

On Tuesday, Trump signed executive actions to advance the approval of the Dakota Access and Keystone XL pipelines -- controversial projects that could see water contamination, a rise in greenhouse gas emissions, and the destruction of Native American land and burial sites.

May's view:

May pledged to ratify the Paris agreement to slow climate change during her first speech to the UN General assembly last year.

But May's commitment to the environment isn't clear.

One of her first acts as Prime Minister shut down the Department of Energy and Climate Change -- folding it into the Department for Business, Energy & Industrial Strategy.