Answer:
It fell to the Turks. Most specifically to the Ottoman turks.
The turks began to advance through the Anatolian Peninsula since the 11th century. A decisive battle was the battle of Mazinkert in 1701 which debilitated the byzantine power in Anatolia.
With time, the turks conquered other places not only in Anatolia, but also in Greece, reducing the Byzantine Empire to its capital, Constantinople, which finally fell in 1453 as stated in the question.
