Turkey's not exactly the flavour of the month in the EU right now, but - as the two sides meet at a summit in Bulgaria - President Erdogan says it's time for the bloc to "keep to its promises."
Ankara kicked off formal membership negotiations in 2005 and, all these years on, they have effectively collapsed.
But there's a reluctance to walk away from each other.
"Europe should take its share of the refugees, so that we don't have to depend on people like Erdogan to manage the issue," said Philippe Lamberts, a Belgian Green MEP.
"That obviously requires a little bit of political courage, but at the end of the day, it's our strategic independence from Turkey."
Erdogan's alarmed the West with a massive purge following a failed coup attempt.
But Turkey remains the destination for many Syrians fleeing war - and an important ally in the NATO alliance. So is it really curtains for the membership bid?
"If Turkey cannot relaunch the reform process and is not anymore in a position to meet EU accession criteria, relations will evolve into a kind of partnership and will be shaped more and more around common interests and strategic priorities," commented political analyst Seda Gurkan.
"And Turkey is considered in Brussels actually as an important strategic neighbour or a key partner rather a candidate."
Three billion euros of fresh cash is expected to be pledged to Turkey to lengthen a deal on it taking in Syrian refugees. And for Ankara, the EU is its biggest foreign investor and trading partner.
"Turkey is not doing very well economically, it needs outlets" said Lamberts, "and it is very clear that bad relations with Europe are harmful to Turkey, so somewhere on the economic level Erdogan needs Europe and Europe in fairness needs Turkey."
With Syria, France has been one of the biggest critics of the Turkish military operation in Afrin - saying border security concerns did not justify it.