At the time Theodosius came to power, the Byzantine empire was divided into east and west. Each half was ruled over by an Augustus, or supreme emperor. This is a remnant of the tetrarchy set up by Diocletian that ended when the empire came to a unified rule under Constantine. Theodosius was a general and military commander under the rule of the Emperor Valentinian. He retired shortly after the disgrace and execution of his father, Theodosius the Elder.
Valentinain was killed in 375 AD. Valentinian II and Gratian, his two sons, succeeded him in the West. In 378 AD, Gratian invited Theodosius to take command of the army in the East where their uncle, Valens, had died at the battle of Adrianople. Valens had no heir so this was ultimately an appointment to Augustus of the Eastern Roman Empire. Gratian was killed in a rebellion in 383 and Valentinian II in 392, after which point Theodosius appointed two of his sons as rulers in the East and West but he ultimately ruled over a unified Roman empire.
Roman emperors generally held off on their Christian baptism until their death because being Emperor required them to do many things that would make them a poor Christian. They also didn't want to be tied to and made to listen to the Church hierarchy. While Theodosius was a Nicene Christian and passed the Edict of Thessalonica (signed by Theodosius I, Gratian, and Valentinian II on 27 February 380) making all Romans profess the faith of the Christian bishops and cementing Nicene Christianity as the state religion, that was minor compared to what followed in his rule. After all, Constantine had also made Christianity the state religion but he didn't persecute or severely punish pagans like Theodosius.
At one point during his reign, Theodosius slaughtered 7,000 Romans in a stadium for their part in a rebellion that led to the death of a local Roman garrison captain. Bishop Ambrose wrote to Theodosius and rebuked him, calling him to repentance. Theodosius went to Ambrose, shed his Emperor garments, and bowed to Ambrose in public penance. Any other Byzantine Emperor simply could have said that Ambrose couldn't call him to repentance as he was simply a "Christian investigator." They could have even had Ambrose put to death for speaking against the emperor. Theodosius, as a baptized Christian, was in a position where he had to listen to the Christian bishops.
Theodosius was violently ill in 380 and thought he was on his deathbed. He was baptized, but then recovered from the illness that he thought would claim his life. His policies from that point on, about 381 AD, were radically anti-pagan and pro-Christian. He reinforced the ban on Roman religious customs, made haruspicy (divination using animal entrails) a crime punishable by death, allowed the criminalization of all local leaders that didn't punish polytheism, and allowed Roman temples to be attacked and looted without recompense.
Between 389 and 392, Theodosius issued a series of decrees that removed non-Nicene Christians from their church offices, turned Roman religious holidays into regular work days, banned blood sacrifices, closed Roman temples, and punished all forms of witchcraft. He also is likely behind the closing of the ancient Olympic Games in 393 AD. Until his death in 395, he continued to persecute pagans and non-Nicene Christians. After his death, the empire split back into east and west.
All I have time to offer here is a brief summary of the rule of Theodosius. For my article on Constantine, the most useful secondary source on his reign was called A.D. 381 by Charles Freeman. I'll link to his book below (it's available as an e-book, paperback, and audio book.)