Kadaïfi is the shredded phyllo pastry that goes in a dozen syrup pastries across the Balkans and Middle East, . In Greece and Cyprus you can by it frozen in bags (it looks like vermicelli).
It’s also the name of the classic pastry of the same name: mixed with melted butter, then filled with chopped almonds (or walnuts or pistachios), cinnamon and sugar, then baked brown and crispy before pouring on a syrup made with sugar, water, honey, rose water and cloves, lemon and cinnamon.
Sometimes it's shaped into little nests called φωλιά κανταΐφι (foliá kantaïfi) and filled with galaktoboúreko. It's also the base for the even more elaborate ekmék.
Images by Apostoloff, Uziel302