NOTE: As always, these borders shifted over the years, may not be entirely accurate, and I naturally rely on published historical sources as the basis of the borders and during what years.
The first centralized state in Persia was founded by Achaemenes, chieftain of the Persians at around 700 BC. They slowly conquered Medes (western Turkey), Babylon, Egypt, and failed in several attempts to conquer Greece. This ancient empire saw Persian control at its greatest extent ever, and in many ways, everything went downhill for Persia from here.
The Achaemenid Empire was destroyed by Alexander and was reformed as his Hellenistic Empire. Upon Alexander’s death the empire fractured, and the Macedonian Seleucid Empire ruled Persia for a century or so until a northern tribe emerged as the rulers of a loose confederacy we call the Partian Empire. Emerging in about 200 B.C., this dynasty held loose control over Persia proper for most of its ruled and spent most of its resources keeping regular Roman invasions at bay.
The Sassanid dynasty was founded by King Ardashir I, who defeated the last Parthian king in the 3rd century. This dynasty ruled the region for three centuries and spread its control across most of the original Persian empire that existed until the invasion of Alexander. However, it was ultimately badly injured by the Byzantine Empire’s expansion in the 6th century, and the last Sassanid Shahanshah (“King of Kings”)lost a 14-year struggle to the early Islamic Caliphate, the first of the Islamic empires. The explosive growth of the Arab Islamic Caliphate coincided with the chaos in Persia, and most of the country was conquered by 650 and subsequently converted. The Sassadnids were the last “Persian” Dynasty to rule the region — all subsequent rulers were Turkic or Mongol, at least until the modern era.
The first real power to diminsh the Islamic Caliphate was the 1037 invasion of the Seljuk Turks from the northeast, forging an empire from Central Asia through Asia Minor.
At the turn of the 13th century the Seljuks lost control of Persia to another group of Turks from Khwarezmia, near the Aral Sea, who ruled as the Khwarezmid Empire for a few brief decades before the invasion of the Mongol Horde.
Following the fall of the Mongols, Persia was ruled by Timur and his descendents.
As that power waned in the 18th century, Persia was ruled by a handful of kings whose centralized power was weak, who were ineffectual at thwarting foreign interests in their country, and while the European powers colonized the globe, Persia only managed to stay nominally independent. This was such that Russia and Britain didn’t even think of communicating with Iran when they divided up the country into two spheres of influence in the Anglo-Russian Agreement of 1907, granting Russia influence over the northern quadrand of the country and Britain access in the east that bordered its colony in India.
Finally, the Iran that we know today had its borders finalized in the aftermath of the division of the Middle East after World War I. And by the request of its rulers, the name “Persia” was dropped in the early 20th century and replaced with “Iran,” which is what we call the country today.
Thus changed the borders of what began as the world’s first transcontinental empire.