Short answers, pulled from the story.
Valens became co-emperor on the 28th of March 364 when his older brother Valentinian I, who had been acclaimed augustus on the 25th of February 364, selected him to share rule of the empire at the Hebdomon outside the Constantinian Walls. Valentinian took the western half; Valens received the eastern half, which included Greece, the Balkans, Egypt, Anatolia, and the Levant.
Valens was killed at the Battle of Adrianople on the 9th of August 378, along with two-thirds of his eastern army, fighting the Goths near Hadrianopolis in Thrace. Ammianus Marcellinus preserves two accounts: in one, Valens was mortally wounded by an arrow; in the other, he was wounded, carried to a wooden hut, and died when the Goths unknowingly set it on fire. His body was never found or given a proper burial.
Valens permitted the Visigoths under Fritigern to cross the Danube in 376 because the Huns had displaced them and they had previously allied with Rome against Athanaric. Valens also calculated that Gothic troops paid in gold or silver would reduce his need for conscription from the provinces, increasing revenues from the recruitment tax. The resettlement collapsed when Roman commanders accepted bribes instead of disarming the Goths as ordered, and then charged excessive prices for food.
The Battle of Adrianople on the 9th of August 378 is recognized as marking the beginning of barbarian encroachment into Roman territory. Ammianus Marcellinus ranked it as the worst Roman defeat since the Battle of Edessa, and the church historian Rufinus called it "the beginning of evils for the Roman empire then and thereafter." J. B. Bury described it as "a disaster and disgrace that need not have occurred."
Valens favored a compromise between Nicene Christianity and non-trinitarian Christian sects; he was an Arian Christian, specifically a Homoean, and was baptized by the Arian bishop of Constantinople before his first Gothic campaign. Modern historians have described Valens as primarily interested in maintaining social order rather than in theological enforcement. He interfered little in pagan affairs, and after his death his successor Theodosius I made Nicene Christianity the state religion and suppressed the Arians.
The Breviarium ab Urbe condita is a short history of Rome from its founding, produced by Valens' secretary Eutropius at Valens' commission. Some historians believe Valens ordered the work so that he, the imperial family, and their appointees could engage more credibly with the Roman senatorial class.