Is this a chance to reset relations between Turkey and the European Union?
A new government in Turkey, and a new European Commission in Brussels, suggests that it could be. But to what end?
EU officials describe the visit led by the High Representative, Federica Mogherini, as the most high-profile for some time.
It is "a strong indication of the strategic importance of the EU-Turkey relationship," Ms Mogherini said ahead of the visit, "and our desire to step up engagement."
Ms Mogherini told reporters in Ankara on Monday that the aim was to "give a sign" that more than ever they needed to increase co-operation because of "common challenges".
Headlines may well focus on discussion of IS militants travelling from Europe via Turkey into Syria; and on Turkish relations with Russia and pipeline politics in south-eastern Europe.
But there is a broader question worth asking: what on Earth are Turkey and the EU trying to achieve together? Is this just shadow-boxing or a serious relationship?
On one level the answer is obvious - they need each other badly. The EU is Turkey's largest trading partner, and Turkey is the EU's sixth largest partner. Many of the goods Europeans buy are manufactured in Turkey.
Turkish plans to exploit new markets to the east as an alternative to closer relations with Europe have also been thrown into disarray by fighting in both Syria and Iraq, and by the failure so far of Turkey's very public campaign to topple President Bashar al-Assad in Damascus.
But while the economic case is clear, the political one is not.
Turkey has been in formal negotiations to join the EU for nearly a decade now, and one senior EU official said that "accession negotiations are still the central pillar" in the relationship between the two sides.
But everyone knows those negotiations have run into the sand.
Only 14 of the 35 "chapters" or policy areas in the Turkish negotiation process have been opened. Last year there was a renewed effort to get things moving again, but it hasn't yet amounted to much.
The division of Cyprus makes things particularly difficult, and many of the policies promoted recently by former Prime Minister and now President Recep Tayyip Erdogan have hardly endeared him to his European partners.
"The vision we have of Erdogan is of someone who has won free and fair elections for 12 years," a senior EU official said.
"But we could never subscribe to what he says about the role of women," - or many other things for that matter.
So will Ms Mogherini make Turkey one of her main strategic priorities? She has a chief of staff who was (briefly) the EU's ambassador in Turkey. It is an issue on which she could stake out some new ground.
There are several policy areas in which progress could be made: visa liberalisation, trade talks and more European help for Syrian refugees.
Some EU member states - the UK among them - are still enthusiastic supporters of Turkey's membership application.
But in other capitals political will is lukewarm at best. Most likely, this will continue to be a rocky ride.