Europe in 1300
Byzantine Empire
The story of Byzantium in these centuries is sad and dreary, culminating with the fall of the city to the Ottoman Turks in 1453. Despite its long decline, Byzantinum—which by this time was little more than the city of Constantinople—was still culturally and economically important.
Byzantium in 1300 was in recovery mode. The city had been conquered by Latin Christians in the Fourth Crusade (1205) and was ruled by them until 1254. A couple of strong emperors in the late 1200s gave some reason to think that the once-great empire might recover at least some of its lost territories.
The emperor in 1300 was Andronicos II, the successor to Michael VIII Paleologus, the restorer of the Empire. He had begun his long reign with strong efforts to get the Empire on a firmer economic footing, even dismantling the Byzantine fleet, but his every effort was dwarfed by larger problems. These were, specifically, the loss of Greece to Catalan mercenaries (a story in itself), and the loss of most of his Anatolian holdings to the rising Ottoman Turks. In the face of these disasters, he spent the last years of his reign simply trying to keep from going under completely.
This, indeed, was the theme for the rest of Byzantine history. An emperor here and there tried to win some tactical victories, mainly through diplomacy, but the advance the Turks was simply too much for the Empire. And while people in the West lamented Byzantium's misfortunes, in the end they did little to stop the Turkish advance, and most of what efforts they did put forth came to nothing or ended in disaster (e.g., the crusades that ended at Nicopolis and Varna).