Image copyright AFP/Getty Image caption The gravitas of the occasion was not lost on the Pope

From tough talk and firm handshakes to the satanic orb and geography lessons, Donald Trump's first foreign trip as US president has not been short of talking points.

There were substantive achievements as well - like the $110bn arms deal signed with Saudi Arabia - but it was the off-the-cuff moments that set the internet abuzz.

Settle down as we round up the highs and lows of his trip so far.

Brussels - Tough talk and a pushy Trump

When Mr Trump arrived in Brussels, he had meetings with EU and Nato leaders. He has previously talked about how Britain leaving the EU is "great" and "fantastic", and how Nato is "obsolete" (before changing his mind).

No surprise, then, that he gave an impassioned speech to the leaders of Nato, telling them to pay their way in the alliance. He also tactfully addressed the victims of the Manchester attack in the UK, lamenting the "beautiful lives" lost, and saying it demonstrated the "depths of the evil we face".

Anyone expecting him to be at his most diplomatic, then, may have been puzzled by an on-camera moment when he appeared to push the prime minister of Montenegro aside at photo time - putting Donald J Trump front and centre.

Media playback is unsupported on your device Media caption Trump pushes past Montenegro's PM

Mr Trump appeared to emerge from the back, and firmly - though not violently - push aside Dusko Markovic, before the US president fixed his coat, ready for the family photo.

It didn't go down well on social media. When JK Rowling tweeted the video, calling Mr Trump "you tiny, tiny, tiny little man", she was retweeted some 145,000 times.

But Mr Markovic, ever the diplomat, said the push was "inoffensive" and it was "natural" for Mr Trump to be front and centre.

Media playback is unsupported on your device Media caption Did President Macron snub Donald Trump in this encounter?

That opinion apparently wasn't shared by France's new President Emmanuel Macron, who veered off course to avoid meeting Mr Trump first - shaking Angela Merkel's hand instead.

But Mr Trump - in an apparently good-humoured and deft move - patiently waited his turn before giving a much firmer and wilder handshake than usual, grinning while he did so.

Melania Trump, meanwhile, spent much of her time in Brussels with sick children, making arts and crafts. She softened plenty of hearts when, on Twitter, she shared her delight at discovering a boy she'd met would get the transplant he was waiting for.

Image copyright AFP Image caption While Mr Trump met with world leaders, his wife spent her time at a children's hospital

The Vatican: 'Glum Pope' and the Catholic FLOTUS

Pope Francis has been mostly smiles during his time at the Vatican - but apparently not when he met President Trump.

On Wednesday, the grin belonged entirely to The Donald while the pontiff came across somewhat stony-faced.

Social media wits joked that he had just learned he would have to listen to Mr Trump confess his sins.

A zoomed out version of the same photo showing Melania and Ivanka dressed in black has meanwhile spawned comparisons with the 1960s US TV series The Addams Family.

Image copyright AFP/Getty

The show featured a family of macabre oddballs who believed they were normal, and was famed for its catchy finger-snapping theme song.

Melania in black at the Vatican. Why?

But all in all, the meeting went smoothly. Other photos showed the pontiff looking more cheerful.

Melania Trump had her rosary beads blessed by the Pope, leading to later confirmation that she is the first Catholic first lady since Jackie Kennedy in the 1960s.

And President Trump seemed to have been inspired, later tweeting that he was "more determined than ever to pursue PEACE in our world".

Middle East: Peach in our time and a presidential first

A White House press statement about Mr Trump's visit to Israel said he would be looking to "promote the possibility of a lasting peach".

In a notoriously troubled region, long-life fruit may seem like an easier goal than an end to conflict.

Image copyright EPA Image caption Israelis viewed Mr Trump's visit to the Western Wall as a sign of support

But Mr Trump's trip to the region was, by and large, a success. He became the first serving American president to visit the Western Wall in Jerusalem, one of Judaism's holiest sites. Israelis interpreted it as a show of support.

But in a speech in front of Israeli officials, he said he believed that Palestinian President Mahmoud Abbas was serious about making peace - and then went to speak with him in a trip to Gaza and the occupied West Bank.

So far, so good. In fact, the oddities during the Middle East stretch were captured in the corner of a camera frame.

The eagle-eyed observers with Israeli newspaper Haaretz spotted Melania Trump swatting away her husband's hand as he reached out for her.

Media playback is unsupported on your device Media caption The 'swat' was captured not long after the Trumps arrived in Tel Aviv

Watch it for yourself - has he got tired of waiting for her to take his hand, and so withdraws it? Or is Melania really swatting her husband away? And did she do it again when they both landed in Rome on Tuesday? Make up your own minds.

If you're one of those people who looks for clues into the health of the Trumps' marriage, this may provide more fodder.

Similarly, the ambassador's facepalm was fodder for body language analysts.

Image copyright White House Image caption That's Mr Dermer on the right, in mid-facepalm

This clip, broadcast by the White House, showed Mr Trump with Israeli officials late on Monday.

He tells them - in Israel, remember: "We just got back from the Middle East", before quickly correcting himself: "We just got back from Saudi Arabia".

You can then see Ron Dermer, the Israeli ambassador to the US, seemingly put his head in his hand, only to quickly correct his gesture and brush his hair.

And lastly, there was the awkward moment when someone forced a selfie upon Mr Trump.

Media playback is unsupported on your device Media caption Mr Trump did not look thrilled with the request for a selfie from Oren Hazan

Towards the end of the long line of people whose hands the Trumps had to shake when they arrived in Israel was Oren Hazan, an MP from the ruling Likud party.

There was just one problem - he wasn't supposed to be there.

Israeli media said he pushed his way through the line of dignitaries - and he then demanded a selfie with Mr Trump. His brazen move had gone down badly with senior Likud officials.

Saudi Arabia: Fighting terrorists and The Orb

Image copyright EPA Image caption The sight of President Trump and his Saudi and Egyptian counterparts around a glowing orb has sparked online jokes

And then there was something that had the appearance of the occult.

It was a surreal sight - President Trump with his Saudi and Egyptian counterparts placing their hands on a glowing globe (they were inaugurating a centre in Riyadh aimed at combating extremist ideology).

It's the image that launched a thousand memes. And when Satanists got involved, you knew things had become especially weird.

Image copyright Saudi Arabia TV/Twitter/@ChurchofSatan

Before he left Washington, Mr Trump's team had touted the speech he would give on combating radicalisation. When he left, Twitter was speaking only about The Orb.

But his speech was, in fact, well-measured, urging Muslim countries to combat radical terrorists and "drive them out of this earth."

He heaped praise on his hosts, blamed their rival Iran, and warned leaders to deal with the ideology that fuels terrorism now - or live with it for generations to come.

Our security correspondent, Frank Gardner, said he went out of his way to avoid the sort of inflammatory language he's more usually known for.

All in all, then, his trip ticked the boxes for diplomatic necessities - and provided sideline entertainment for the cameras.

Given some of the speculation in the media ahead of the trip, a lack of any clear disasters could be considered a success.