The knights of the Fourth Crusade set up a Crusader kingdom known as the Latin Empire or Romania based on Constantinople after sacking the city in 1204, with the intent that it would be a Roman Catholic successor of the Byzantine Empire. Baldwin IX, Count of Flanders, was crowned the first emperor May 16, 1204.
The Latin name of the emperor was Imperator Romaniae, or Emperor of Romania. This name, which loosely means "Romanland", has nothing at all to do with the modern country by that name; rather, it was the Latin form of the title of the so-called Byzantine Emperor, whom the Latin Emperor hoped to replace (the Byzantine Empire was never called that, and the Emperor's title was Basileos Rhomaion, or Emperor of the Romans). This has the curious effect of creating three Roman Empires in Europe at the same time.
Although the state layed claim to all of the lands controlled by the Byzantine Empire at the time Constantinople was conquered and did exert control over areas of Greece (the Crusader States: the Kingdom of Thessalonica, the Principality of Achaea and the Duchy of Athens), much of the territory remained in the hands of rival states led by aristocrats of the former empire, such as the Despotate of Epirus, the Empire of Nicaea, and the Empire of Trebizond. Although the relatives of Baldwin, Count of Flanders struggled for many years for their domain, it came to an end on July 25, 1261 when Michael VIII Palaeologus recaptured Constantinople, deposing the last Latin Emperor, Baldwin II.
For about a century thereafter, the heirs of Baldwin II continued to use the title of Emperor of Constantinople, and were seen as theoretical overlords by the various remaining Latin states in the Aegean.
Latin Emperors of Constantinople, 1204-1261
Titular Latin Emperors of Constantinople, 1261-1383
(Jacques willed his titular claims to Duke Louis I of Anjou, also claimant to the throne of Naples, but Louis and his descendants never used the title.)