In 313, Christianity and all religions were free to be practiced in the empire, but a few years later, in 330 the empire split in two, with the western capital in Rome and the eastern in Constantinople (Istanbul, Turkey).
Rome slowly deteriorated, but was saved by the Catholic Church, when in 800 the church crowned Charlemagne the Emperor of the Holy Roman Empire in exchange for giving the church power in Rome and throughout the empire. The church offered Charlemagne power in that they controlled a unifying force, Christianity, which much of Europe had converted to by this point. However, it also shifted power from Rome to France and severed ties with Constantinople, putting Rome itself, and much of present-day Italy in further decline.
For centuries after this time, much of Italy fell under the rule of the Holy Roman Empire, but various city-states maintained much independence and self-rule. As the Holy Roman Emperors and the Popes fought over power, each city-state sided with whomever would give them more autonomy, creating further division, but also seeing the rise of prosperity to numerous cities such as Venice and Florence (to learn more about the history of the pope, Vatican City, and the Papal States, read the History of Vatican City).
During this period, until the 1400s there was generally no united country, but small independent states, often times at war with each other as power struggles regularly erupted.
Beginning in 1453 with the immigration of Byzantium scholars, Italy, particularly Florence became the center of the Renaissance, which brought new architectural styles, arts, and thinking to first Italy, then much of Europe.