Constantinople (once founded as Byzantium) was the capital of several countries - that of the Byzantine Empire first, for a short time of the Latin Empire, and finally after their conquest of the Rum-Seljuks.
In 1204 (as OTL), during the Fourth Crusade, the Byzantine Empire was conquered and Constantinople plundered. For many years, the Orthodox people suffered under the fate being servants of the Roman Catholics.
Finally in 1276, Constantinople was conquered by Nikaia (some defenders had changed sides, after receiving a big bribe). The Latin Emperor fled to Athens. Nikaia's energy and power wasn't sufficient for further attacks on Epirus and other Crusader states, however. Emperor Michael had to start talks with the west about a reunification of the churches.
Roman king Ottokar I died in 1286 while in Constantinople with his army, having planned another crusade.
In 1327, Constantinople fell after a long siege, effectively defeated by the hunger. Many Byzantines fled, parts to free Greek states or Trapezunt, others to Italy (mostly Florence, Genoa and Milan, avoiding Anjou Naples, the Papal States and Venice), again others even to Kiev. The knowledge they brought to Western Europe helped spawning the "Rinascita" (it wasn't called that at this time) that already started in the last century. Genoa lost access to the Black Sea, suffering economic decline in the following years.
Since 1575, Muslim refugees from Naples (mostly merchants replaced by the Florentines, but some scientists too) arrived in Constantinople.