It gives students the chance to study and gain experience abroad. But, if Brexit Britain crashes out of the EU without a deal, the Erasmus plus programme could be over in the UK.
In Brussels, students at the ULB university are still applying to head across the water - for now.
"For us, we have to start looking for other destinations should there be a hard Brexit. Looking into Canada, Ireland being potential destinations," said Kristin Bartik, ULB Vice-Rector.
"And for some of our students, Northern European countries, Scandinavian countries might be a potential alternative. But it would be still be a pity that it's not the UK."
One student, from London, reckons a hard Brexit will be a blow to both sides.
"If Brexit did finish without a proper deal, it would be a huge loss not only for the UK, but also for Europe I feel. Because people come over to the UK for the education system, to learn English, to experience the UK, so I think it would be a big shame in my opinion," said Emma J Latham, in Brussels.
Britain wants to keep Erasmus, says one UK Tory MEP in Brussels - but a finance deal needs to be struck.
"As I understand it, the UK government wants to continue Erasmus as it currently exists, so along the same lines. There are obviously questions about budgets, who is going to pay, what the input in budgets are," said Daniel Dalton.
"There is also the question, many more European students come to the UK than the other way around, so the cost for the UK government are often higher, than for European governments; These figures need to be sorted out. But the principles, and I think we are still at the basic principle stage, is that the UK government wants to stay in Erasmus."
Erasmus is just one example of what's at stake as the Brexit talks continue.