Roman Emperor Theodosius I, dies on January 17, 395 CE. He bequeathed the Eastern half to his son Arcadius and the Western half to his son Honorius, marking the permanent split of the Roman Empire. The East eventually became the Byzantine Empire and the West collapsed within a century.
The Western Roman Empire collapsed due to a combination of factors, including invasion from Germanic tribes, internal political instability, economic issues (overspending, heavy taxes, reliance on slave labor), and a widened gap between rich and poor. The traditional "fall" of the Western Roman Empire is thought to be in 476 AD when Romulus Augustulus, the last emperor, was deposed by the Germanic general Odoacer. Many Roman culture and institutions, especially the Church, persisted as they transformed into medieval Europe. The Eastern Roman (Byzantine) Empire continued for another thousand years.