After Emperor Romanos captured Manzikert, instead of sending out each of his regiments to be slaughtered by the Turks, he assumed their army was very large. Romanos stationed most his armies in the hills, leaving a small army as a decoy. As the Suljuks swooped in to attack the decoy, the rest of the Byzantine army ambushed the Suljuks from the hills, raining down arrows and rolling boulders down. The entire Suljuk army was either killed or taken prisoner, and Alp Arslan, sultan of the Suljuks, was killed. After leading further campaigns, the Suljuks surrendered to the Byzantines, ceding significant territories. Once Romanos returned to Constantinople, he began working on his original ambition of reforming the Byzantine army. By his death in 1092, he had imposed significant reforms in an attempt to reduce both army and governmental corruption. His son and successor, Nikephoros II Diogenes, enacted heavy reforms which further stabilised the Empire. The Second and Third Crusades did not happen, as the threat of a Muslim conquest of Anatolia was seen as highly unlikely with the reformed and very strong Byzantine military. By the 1400s, Byzantium was still mostly prosperous, and had maintained stable borders, owning the southern Balkans and Anatolia. The renaissance began both in Byzantium and in Italy, with the arts and culture being strongly promoted. Constantinople's population rose to 220k by 1400, making it the most populous city in Europe and one of the most populous cities in the world. As the eastern trade routes did not fall, colonisation of the Americas was delayed until 1542, when Portuguese merchants accidentally diverted West to the Americas. 

By 1600, Rhomania was still very wealthy, although they had stagnated in wealth compared to Western Europe. By that point, Constantinople had a population of 800k so it was still the world's most populous. In an attempt to foster trading, they sent an army to occupy what is now the Suez canal, and began work on the project. The enlightenment and later the industrial revolution spread to Byzantium about as fast as it did to Italy, and soon enough the Roman national identity was founded as the successors of Ancient Rome. The emperors decided to reduce their authority as time went by, and by the mid 19th century they were a constitutional monarchy. As Africa and the Middle East began to be partitioned, the Romans attempted to establish their own colonies. They were granted the Levant by the conference, although they had trouble actually subjugating it. They grew massively throughout the 19th century like every other European power, and Constantinople reached a population of 3.8 million by 1850.

By the 20th century, the Romans had joined the Central Powers so to expand in the Balkans, and when WW1 started, due to having another strong, industrial economy, the Central Powers won by 1920. Austria-Hungary formed the Danubian Confederation soon after, and the Russian territories were released and puppeted by Germany. Constantinople grew significantly in the years following the war, reaching the modern population of 22 million, a GDP of about 1.5 trillion, and a GDP per capita of 68.1k. The entire nation of Rhomania has a population of 142.8 million, and a GDP of 9.45 trillion. This makes Rhomania the 4th largest economy in the world, below the United States, Chinese Republic, and German Empire. 

Imperial Rhōmanía, as per Google Maps - What if Byzantium massacred the Seljuks in 1071?