Brexit: What does MEPs' vote tell us about talks progress?

Major players? Michel Barnier and Nigel Farage

Members of the European Parliament have been voting on last week's Brexit deal during their monthly meeting in Strasbourg.

Their view is important, because MEPs will have a decisive say on the final agreement.

Here are six things we learned from their session on Wednesday.

MEPs are happy for the talks to move to the next stage

Around 80% of the European Parliament voted for the motion which said there had been enough progress in negotiating the UK and the EU's divorce that it was time to start talks about a transition period and the future relationship.

The European parliament feels that it convinced the UK to be more generous about which EU nationals get to stay in Britain after Brexit, in particular spouses, and children who have not even been born yet.

There are still concerns about the rights of EU nationals

MEPs have made this their priority issue. They are particularly worried about the application process that EU nationals will have to go through if they want to stay in the UK after Brexit.

Anti-Brexit demonstrators protested outside the UK parliament

The government says it should cost the same as a new passport - £72.50. Parliament's Brexit co-ordinator Guy Verhofstadt said it should be free so it is as accessible for a plumber as it is for a banker.

Will these be deal-breakers when the Parliament gets a formal vote on the final Brexit Agreement at the end of 2018, or will MEPs come under enormous pressure to wave it through as the clock ticks down?

• Reality Check: Theresa May's deal with Brussels

• How do you work out the Brexit bill?

David Davis a hot topic - and he was not even there

The Brexit secretary's comments that the government could change its mind about what has been agreed so far have come up a lot.

MEPs voted in favour of an amendment which said he risked undermining the good faith that has built up between both sides, and which reminded the government that they have to stick to their promises if they want to make good progress in the next phase of talks.

Is Nigel Farage preparing for ANOTHER referendum?

The former UKIP leader still chairs one of the political groups here, which gives him a prime speaking slot.

He went on an epic rant about how "Theresa the Appeaser" had bowed to all of the EU's demands, which he claimed would lead to continued immigration from Europe.

A future government could keep the UK in the single market too.

"I fear we will have to fight for Brexit all over again," he said. Is he gearing up to force a referendum on the final Brexit deal if it is too soft for his liking?

MEPs have other things to worry about

The second most talked-about-subject after Brexit was a letter sent by the President of the European Donald Tusk who chairs the summits of EU leaders.

It talked about reforms to how the EU handles asylum seekers - proof that the EU has other things on its mind, despite Brexit.

Michel Barnier looks very happy

The chief Brexit negotiator gave me a cheerful wave and his biggest smile yet.

Either sufficient progress suits him, or he loved the praise that was lavished on him by MEPs.

Alternatively, maybe he is just looking forward to some skiing back home in the French Alps, after six months of gruelling negotiations.