In one of today's more unusual scenes, a host of "pregnant Trumps" were protesting in Helsinki:

The protesters main target is the so-called "global gag" rule, which was reinstated by Donald Trump in 2017.

The policy requires non-governmental organisations that receive federal funding to agree to "neither perform nor actively promote abortion as a method of family planning in other nations".

The policy does not directly affect services in the US - but it does impact women in developing countries, where funds or facilities are already limited.

• Read more: Trump's order on abortion policy - what does it mean?

Germany's foreign minister has said Europe cannot rely on Donald Trump and needs to close ranks after the US president called the European Union a "foe" with regard to trade.

"We can no longer completely rely on the White House," Heiko Maas told the Funke newspaper group.

"To maintain our partnership with the USA, we must readjust it. The first clear consequence can only be that we need to align ourselves even more closely in Europe."

He added: "Europe must not let itself be divided, however sharp the verbal attacks and absurd the tweets may be."

James Robbins
Diplomatic Correspondent

Image source, EPA

The two leaders looked serious as they sat down side by side.

Each made introductory remarks to the press through their interpreters who will be alone with them during an opening session of talks without advisers.

President Putin spoke first, saying there were enough difficult multinational issues that they needed to discuss them.

President Trump started by congratulating Vladimir Putin for hosting an extraordinary World Cup.

He said that the two countries had great opportunities together after not getting along very well and he thought they would end up having an "extraordinary relationship".

But hours earlier, a tweet from President Trump blamed the United States for bad relations with Russia.

That is likely to alarm White House advisers, already nervous about the risks of giving too much credit to Vladimir Putin during this encounter.

Image source, Reuters

Mikhail Kasyanov was Russian prime minister under Vladimir Putin from 2000 to 2004 and now leads - in exile in the US - the opposition People's Freedom Party.

He told the BBC that while Mr Putin will be seeking a "softer attitude" from the US, he does not believe Mr Trump will offer sanctions relief.

"That's why just I think that it will be PR actions for both presidents," he said.

But he warned that both leaders are unpredictable.

"In Russia, we have an authoritarian regime. It means everything depends on the leader. And Mr Putin is prepared for everything, any moment," he said.

"But Mr Trump also stolen from Mr Putin such important feature(s) like unpredictability, and right now, just, people don't quite understand what could happen."

Image source, AFP

The Russian president meets the American president - in Finland. Why Finland?

It has a history of having good relations with both countries, and hosted summits between the United States and the former Soviet Union during the Cold War - in which it stayed neutral.

It shares a significant stretch of border with Russia, and maintains good relations with its government.

It's also not a Nato member - and Russia has had a rocky relationship with the military alliance at times.

And it's geographically convenient, being a short flight for both from their previous engagements in the UK (for Mr Trump) and Moscow (for Mr Putin).

CNN - a favourite target of Mr Trump's ire - has been asking why the president is speaking behind closed doors, one-on-one.

Its White House team says Mr Trump wanted a direct meeting, with no leaks or interventions from others - and that there may not be any records kept of what is said;

Some social media users are apparently unimpressed by the Trump-Putin meeting in Finland today.

It seems like Twitter discussion about the meeting has been hijacked by the hashtag "treason summit" - which is trending on Twitter worldwide.

Here it is at the top of the US list:

Image source, Twitter

The meeting has been particularly controversial as the US is currently conducting a high-level investigation into alleged Russian meddling in the 2016 election, which Mr Trump won.

On Friday, the probe announced charges against 12 Russians for their alleged role in the hacking of Democratic officials in the months before the vote.

In light of this, many have been left questioning why Mr Trump is still taking part in today's meeting.

Image source, Reuters

Here's what President Putin told President Trump, in Russian:

"Distinguished president, it's a pleasure to meet you here on hospitable Finnish soil in Helsinki," he said.

"We continue to have regular contacts - we have talked on the phone and met several times at various international events.

"But of course, now it's time to talk in detail about our bilateral relations and various problem areas in the world. There are a lot of them."

The BBC's Steve Rosenberg in Helsinki tweets about the advertising that has popped up all over the city in advance of the summit:

The editor of Finland's Helsingin Sanomat newspaper, Kaius Niemi, tweeted this explanation yesterday:

Donald Trump and Vladimir Putin ended their brief remarks to the press with a handshake - which you can see here:

Now, while Mr Putin is known to use lateness as a power play, Mr Trump is known to use his handshake to assert dominance in a situation.

But a couple of Trump-watchers have noticed it wasn't quite as fierce as in previous meetings with other world leaders:

President Donald Trump has congratulated his Russian counterpart on a successful World Cup, before outlining some of the subjects they would touch on during today's meeting.

"I would congratulate you on a really good World Cup, one of the best ever," Mr Trump said.

Mr Trump, whose words were translated into Russian for Vladimir Putin, said they would discuss "everything", from trade to military to China.

He added: "We [the US and Russia] have not been getting along very well... it’s getting close to two years.

“Getting along with Russia is a good thing, not a bad thing.”

Mr Trump also said he hoped they could "do something" about their nuclear arsenals.

Now they have both finally arrived, Donald Trump and Vladimir Putin will begin a one-on-one meeting.

Here is a picture of the two of them together:

Image source, Reuters

The original schedule had the two presidents sitting down for an hour-long one-to-one, followed by a working lunch, potentially with other diplomats.

A press conference was due to be held in two and a half hours' time, with President Trump due to depart Helsinki airport shortly afterwards.

We don't yet know if the late start changes that plan.

Donald Trump has arrived at the presidential palace in Helsinki, where he is meeting Russian President Vladimir Putin.

They are now an hour behind schedule.

A second motorcade has been spotted heading to the presidential palace, suggesting Donald Trump is now en route.

He was reportedly refusing to leave his hotel until after Vladimir Putin, who was more than half-an-hour late himself, arrived at the venue.

The power-play between arguably the world's two most powerful men has not impressed everyone:

Russian-language news outlets Tass and RIA Novosti are both leading their coverage on the angle from Mr Trump’s earlier tweet, in which he said “years of US foolishness and stupidity" are responsible for the poor relations between the two countries.

Even the country's foreign ministry picked up on the remark:

So what does Russia expect from today?

Kremlin spokesman Dmitry Peskov also gave an interview to the state-backed broadcaster Russia Today - saying Russia hopes the summit will help to heal the rift between the two countries.

“This approach has to be based on commitment to develop mutually beneficial cooperation… this is what we hope to achieve at this summit,” he said.

“We hope this will be a baby step towards overcoming the current critical situation in our bilateral relations,” he added.

Footage shows the Russian leader arriving at Finland's presidential palace.

It has been reported that Donald Trump is waiting for Vladimir Putin to arrive at the venue before he even leaves his hotel.

Mr Putin is often late for meetings with other high profile world leaders, with some suggesting this allows him to assert his dominance.

Even a direct line to a higher power doesn't stop him: he has been late to two meetings with the Pope.

BBC Monitoring
The world through its media

According to Russian state TV’s Channel One, the meeting between Vladimir Putin and Donald Trump is the "intrigue of the year", and the very fact the summit is taking place at all is of "colossal significance".

Another Kremlin-run television channel, Rossiya 1, describes the meeting as the "main political event" of the summer, which will overshadow Trump's appearance at the Nato summit this week and his controversial visit to the UK.

"The show is over. Now the work begins. After all, he was just passing through Brussels and London on his way to Helsinki," Rossiya 1 says.