In 276 BCE a grandson of one of Alexander's generals, Antigonus Gonatus, established a new dynasty in Macedonia known as the Antigonid Dynasty.
The Seleucid dynasty was the largest of the Hellenistic dynasties, and occupied most of the territory formerly controlled by the Persian empire, however, the size of this monarchy eventually lead to trouble, as the Seleucids had some difficulty in controlling it's eastern boundaries.
Ptolemy became king in 305 BCE and established the Ptolemaic dynasty of pharaohs.