What is this meeting all about?
German Chancellor Angela Merkel, French President François Hollande, Spanish Prime Minister Mariano Rajoy and Italian Premier Paolo Gentiloni are tyring to draw up a plan for Europe after Brexit.
The meeting came in the run-up to celebrations on March 25 of the 60th anniversary of the Treaty of Rome, which founded what would eventually become the European Union.
Are the leaders expected to outline a way forward in the coming weeks?
Not really, but there's much talk of a "multi-speed" Europe. The idea has been gaining traction over the past few months in Brussels.
It was also one of the five options for the bloc's future of European Comission president Jean Claude Juncker's White Paper. France and Germany have already commited to this vision.
"This logic will replace this idea of ever closer integration for all," says Yann-Sven Rittelmeyer, a Policy Analyst with the European Policy Centre. "We'll have what kind of differenciation will be proposed. We'll have to see if this process will follow European Union treaty rules."
What would a multi-speed Europe look like?
In a sense, the European Union is already multi-speed because not all of EU members are part of the Eurozone or the Schengen area.
"Let's not fool ourselves, we already have a multi-speed Europe," notes Thorsten Benner, the co-founder and director of the Global Public Policy Institute.
"We already have variable geometry if you will. So with the preferences of different EU member states in terms of closer integration in one area and not so close integration in another area, differing so much, I think going forward in that direction is the only way to keep the EU afloat."
Concretely, countries wanting to move ahead on issues such as economic growth, border protection and defence could form smaller groupings, leaving reticent members behind.
"We have already witnessed some progress in some areas," says Yann-Sven Rittelmeyer.
"It's clear that defense and military spending is right now, the favoured area to move forward. We have seen last year some progress being made thanks to a Franco-German impetus. I think the creation of a joint military headquarters would be another important step."
When can we expect a concrete plan any time soon?
Probably during the Rome summit set for the end of this month.
While Italy, Belgium, the Netherlands, Luxembourg as well as France and Germany have all signed up to this idea, Eastern EU members remain reticent.
That's particularly true of the Visegrad group, comprised of Hungary, Poland, The Czech Republic and Slovakia.
"It's a pity that the Polish government isn't part of [yestrerday's] Versailles meeting", says Thorsten Benner.
"I do think that the Visegrad member states would be open to a multi-speed Europe provided that they're not left out of areas they care about. You already have a lot of imbalances with the EU."
With elections looming ahead in The Netherlands, France and Germany - and potential wins for populist parties - it makes it all the more urgent for the EU to move quickly on this.
The bloc, however, has a reputation for moving at a snail's pace.
"Let's face it, the EU is in the biggest crisis since its founding, so we need a flexible way forward," says Thorsten Benner.