The Christianization of the Roman world occurred gradually over several centuries.
Constantine the Great (d. 337) was the first Roman emperor to adopt Christianity and to give the Church official status in the Roman Empire. Constantine instituted the Edict of Milan in 313 CE that allowed the freedom of worship for all in the empire. Constantine went on to create the city of Byzantium (later renamed Constantinople) in 324 CE that would become the capital of the Eastern Roman Empire.
It was during the reign of Constans, the youngest son of Constantine, that the first prohibition of pagan sacrifice is found in a law code in 341 CE. According to this prohibition, “The madness of sacrifices shall be abolished. For if any man in violation of the law of the sainted Emperor, Our father, and in violation of this command of our Clemency, should dare to perform sacrifices, he shall suffer the infliction of a suitable punishment.”
It is not clear exactly to who this law was directed, although it could have included not only pagans but too soothsayers and those who used other magic practices. This law was also not rigorously policed and it seems that sacrifice continued in Rome. Several additional laws were issued between 353 and 360 CE in which the prohibition of sacrifice on pain of death was reinforced and the venerating of pagan images and divination outlawed.
It was under the reign of emperor Theodosius I (r. 379-395) that Christianity became the official state religion. Theodosius instituted severe legislation against paganism in the empire which saw practices like public and private sacrifice, the decoration of sacred trees, and the creating of turf altars made treasonable crimes. Pagan holidays dedicated to the gods were made normal working days. Despite this, the old Roman pagan religions continued to be practiced by the urban elite and the rural common people. Even by the time of Theodosius’s death, roughly half of the Roman population, it has been estimated, was still pagan. It was becoming clear, however, that being pagan seemed unprofitable in career terms as Theodosius’s successors continued to institute laws against paganism. For instance Emperor Leo I banned pagans from the legal profession around 468 CE. There did remain some religious toleration in the Byzantine Empire during the fifth and early sixth centuries, especially under the reign of Anastasius (r. 491-518). Various cities and towns, including Athens, Alexandria, Gaza, and others, remained centers of Hellenic pagan thought and practice.
Paganism experienced further affliction under the reign of Byzantine emperor Justinian I (r. 527–565). Under Justinian, orthodox Christianity was imposed on his subjects and pagans were made to report to churches to be baptized and receive Christian instruction. If this was resisted, the penalty would be the confiscation of property and the loss of citizenship. Christians caught practicing pagan rituals could face the death penalty. Further, the schools of Athens were closed in 529 CE, the works of the classical thinkers were devalued, non-Christians were banned from teaching, and there are accounts of pagans being prosecuted in Antioch between 554 and 559. The guilty could face various punishments including working in hospitals, imprisonment in monasteries, or execution.
We also have accounts of the desecration and destruction of pagan idols, objects, and images. It seems that pagan idols, images, and objects had little value except in the aesthetic sense, such as in the case of high-quality sculptures.
The destruction of these items was a demonstration of the power of Christianity over the old pagan gods. The Coptic monks in Egypt were particularly zealous; for example, Abbot Shenoute (348-465), who came from a desert monastery near Thebes, speaks of how he went into a pagan village and “entered the temple and smashed the idols which had been cast down one after the other.” On another occasion along with his fellow monks, Abbot Shenoute entered a shrine containing idols and “picked them up, took them down to the river, smashed them in pieces and threw them in the river.” In 489 CE, monks destroyed the Isis cult of Menouthis and burned many of the images and idols they found in front of local people.
Davies, Owen. 2011. Paganism: A Very Short Introduction. Oxford University Press.
Bradbury, Scott. 1994. “Constantine and the Problem of Anti-Pagan Legislation in the Fourth Century.” Classical Philology 89(2):120-139.