Understanding the Holy Roman Empire

The first time I heard the phrase the "Holy Roman Emperor" I was reading a biography of Catherine the Great.  I was immediately confused.  Roman?  Didn't Tsaress Catherine rule in the eighteenth century?  Why "Holy" Roman?  Was this northern Italy or something?

Only now am I grasping the essence of the Holy Roman Empire.  In the 3rd century AD the Roman Empire had split into the eastern and western empires.  The eastern part was still intact with its culture and emperor, whereas the western portion was soon overrun by barbarians, so much that Rome was sacked in 410.  Now, Rome only existed in the east, and Byzantium was its capital.

Time goes on and the eastern and western churches have petty theological clashes, which would later result in an Orthodox and a Catholic Church, as opposed to "the church."  Rome, which I now refer to as the Byzantium Empire, experiences both good and bad emperors...

...and bad empresses.  One of these was Empress Irene, who began as a regent for her son Constantine VI, but then decided to keep the throne for herself by blinding her son and sending him to a monastery to live out his remaining years.  Now, Pope Leo III did not want Irene to represent Christianity or Rome, and so when Charlemagne conquered Italy, Pope Leo crowned Charlemagne himself.  And here is the important part.  He didn't just crown Charlemagne king of Italy, nor was he crowned the emperor of Western Rome.  Charlemagne was crowned emperor of all of Rome, including the eastern portion of the empire.  Consequently, in the mind of Pope Leo, the capital of Rome was now moved to western Europe, and specifically, to the Frankish Kingdom over which Charlemagne reigned--almost all of western Europe.

After Charlemagne's death his empire fractured and evolved such that the Franks had their own kingdom in modern-day France, and modern-day Germany became a region holding numerous autonomous duchies.  These duchies had an emperor they sometimes elected, and at other times was dynastic.  However, all Holy Roman Emperors had to receive the Pope's consent, and thus, it continued to be called the Holy Roman Empire...

and remained the Holy Roman Empire from the 10th to the beginning of the 19th century!