On his deathbed, some historians claim that when he was pressed to name a successor, Alexander the Great muttered that his empire should go "to the strongest". Other sources claim that he passed his signet ring to his general Perdiccas, thereby naming him successor, but whatever his choices were or may have been, they were ignored. Alexander's generals, all of them with the loyalty of their own corps at their backs, would tear each other apart in a vicious internal struggle that lasted almost half a century before four factions emerged victorious: Macedonia, the Seleucid Empire in the east, the Kingdom of Pergamon in Asia Minor, and the Ptolemaic dynasty in Egypt. During the course of these wars, Alexander's only heir, the posthumously born Alexander IV, was murdered, extinguishing his bloodline for ever.

Despite the infighting among them, one thing Alexander's generals did agree upon was their Hellenistic culture. Most famously, Ptolemy's line firmly established the Hellenistic culture of the Greeks while ruling over Egypt, and by marrying within their family line, the Ptolemaic pharaohs kept their Hellenistic heritage until the very end of Ptolemy's line, which died with Cleopatra in 30 BCE. Although the Seleucid Empire is less well known, Alexander's general Seleucus was no less successful in "Hellenizing" Persia and parts of Asia Minor. The Greek influence is still readily visible in the region thousands of years later.