The Galactic Emperor was the head of state of the Galactic Empire. Its power and authority were mainly derived from those of the Supreme Chancellor and the additional rights bestowed upon that office by the Galactic Senate during the Separatist Crisis and Clone Wars, though greatly enhanced and expanded to fit the role of supreme dictator.
Emperor Palpatine's official heir would normally be Darth Vader as his Sith apprentice; however, there were indications that he never intended this to happen — he wanted Vader's son, Luke Skywalker, to take his father's place on Palpatine's side by killing Vader.
In the Declaration of a New Order, Palpatine's speech had indicated that the Imperial Senate would elect the Galactic Emperor, but no one in the Imperial High Command had any desire to restore a body that would probably dissolve the Empire, so many Imperial commanders became rogue warlords after the Battle of Endor.
Many warlords would take the title of Emperor in the wake of Palpatine's death, but it wasn't until 8 ABY that a true successor to Palpatine arose. As of 15 ABY, the Emperor is the enigmatic Aleister Vadim.