This from our White House reporter, Tara McKelvey:

"The Russian state has never interfered, and is never going to interfere" in external elections, Putin says.

Trump brought it up, he said.

Mr Putin also called for more cooperation in Syria, where military strategy between the two nations has sometimes been at odds.

He also lauded the “personal engagement” of Mr Trump in the Korean peninsula - which resulted in talks with North Korea's leader, Kim Jong-Un.

But he said they did not agree on all issues.

Vladimir Putin spoke first, and said he had made firm proposals on arms control.

“As nuclear powers, we bear special responsibility” for international security, he said.

He said Russia considered it necessary for the two countries to work together on nuclear disarmament and non-proliferation – and to avoid weapons being placed in space.

This is where things get exciting, if previous press conferences involving the US president are anything to go by.

We've embedded a live stream of the press conference in the video player at the top of our live page, if you'd like to follow along.

A man was just bundled out of the room by security, waving a stack of paper.

Our reporter in the room identified him as a journalist working for The Nation (from the US) - and apparently the US Secret Service took part in his removal.

Not yet clear why.

The BBC's Moscow correspondent Steve Rosenberg tweets:

It's the only show in town this afternoon - we are all waiting for this press conference to start.

Each of the news wires are running pictures from inside the room where it will begin imminently:

The last time President Vladimir Putin held a joint press conference with a US leader was way back in 2008.

He missed the 2009 and 2010 sessions because he was prime minister at the time.

Expectations are high.

John Brennan, the director of the CIA from 2013 to 2017, has tweeted about today's meeting between Donald Trump and Vladimir Putin - and he isn't happy:

Michael McFaul, a former ambassador to Russia for two years during Barack Obama's presidency, has been tweeting his reaction to the day's events so far.

A "valiant" official is trying to herd reporters into the room where Donald Trump and Vladimir Putin will be speaking this afternoon.

It is not necessarily an easy job, tweets Tara McKelvey:

Does this mean a press conference is imminent?

Image source, AFP

While Donald Trump and Vladimir Putin are enjoying a delayed lunch, let's take a look at who else is at the table.

So, going along the American side, we have:

• Russia expert Fiona Hill
• US Secretary of State Mike Pompeo
• US President Donald Trump
• US Ambassador to Russia Jon Huntsman
• National Security Adviser John Bolton
• Out of shot is John Kelly, the White House Chief of Staff

On the Russian side, we have:

• Putin’s press secretary Dmitry Peskov
• Foreign policy aide to president Yuri Ushakov
• Russian President Vladimir Putin
• Foreign Minister Sergei Lavrov

• Russian Ambassador to Washington Anatoly Antonov
• Head of North America dept of Russian foreign affairs ministry Georgy Borisenko

Donald Trump will bring up meddling in the 2016 election, a US official has told the BBC's Tara McKelvey.

He will also bring up the issue of the annexation of Crimea, she tweeted:

Mr Trump mentioned neither of these things when he outlined what the two would be discussing earlier.

It is also not on the list of topics given out by the Russian Embassy in the US a short while ago.

However, if he does address the election issue, it will likely calm some of his critics who are tweeting using the hashtag #TreasonSummit.

As the two presidents sat down for their working (and very late) lunch, Mr Trump said his private meeting was a "very good start".

No hints were given as to what was discussed.

In the last few minutes, Russian news agency Interfax reported that it has finally ended - with pictures from the venue showing diplomats sitting down to lunch.

Journalists had been told the the one-on-one meeting between the presidents was still ongoing after two hours.

That means it ran over time by more than half-an-hour. It was also more than an hour late starting - and is due to be followed by a second meeting involving other senior officials.

So exactly when the press conference - which should have started almost 10 minutes ago - will take place remains unclear.

This meeting had no formal agenda, but the Russian embassy in Washington DC has tweeted what it says are the planned topics:

• Normalising bilateral relations
• Ukraine
• Syria
• The Korean peninsula
• Terrorism

Mr Trump mentioned none of these in his own remarks - pointing instead to trade, China, military issues, and nuclear proliferation.