With the accession of Valentinian I in the West and his brother Valens in the East in 364 AD, the split between the East and West of the Roman Empire was reaching it's conclusion. The West was facing not just military incursions of the "Barbarians" such as the Goths and Vandals, but the settling of Roman land by them as feoderati, i.e. by treaty, and infiltration of government by educated "barbarians"
In 378 AD, Valens was defeated at Adrianople, by armies of the Visigoths and Ostrogoths, when two thirds of the Roman army of the East were destroyed. The situation was saved by the elevation of Theodosius I as emperor in the East.
During the reign in the West of Honorius (293-423 AD), Rome was sacked. In 410 AD Honorius wrote to the citizens of Britain telling them to look out for themselves.
The emperors in Rome became little more than puppets of "barbarian" masters and in 476 AD, Odovacar was proclaimed king and sent the regalia of the infant emperor, Romulus Augustus, to the Eastern emperor, Zeno, declaring that the West no longer needed a separate emperor. This was the effective end of Rome in the west, although territory was re-captured by eastern emperors, only to be lost again.