The whole empire was divided to some of his generals (Antiochos, Seleukos, Ptolemaios, Antipatros and some others who inherited smaller territories) who in the course of time lost the land against local forces, or the Romans (later on).
When Alexander died in 323 BC he had no legitimate heir and so on his death bed, surrounded by some of his generals who questioned him for a successor, it is said that he whispered 'to the strongest' although some might interpret this as 'Krat'eroi' one of his favoured generals - Craterus - who wasn't there at the time. This led to confusion and despair amongst his generals who then accused each other of poisoning Alexander who was just one month short of being 33 years old. Eventually this led to the assassination of Craterus before he could take over the empire. The empire was then contentiously split amongst his successors who were known as the Diadochi and the infamous (four) Wars of the Diadochi and the beginning of the Hellenistic period.
If you google 'Diadochi' you will find sources for the timeline of the break up of his empire and the Greek revolt (Lamian war).