Why is the Pantheion such an amazing building?
When the barbarian hordes sacked Ancient Rome, they destroyed every one of its temples--except the Pantheon, the temple of all Gods. Why did they leave it untouched? They couldn't understand how such an enormous dome could ever have been built. Some say, they were actually frightened by it, thinking Gods really did live inside it with awesome powers, and they would be struck dead if they desecrated it.
Built under Emperor Hadrian in 126 AD, the Pantheon not only embodies some of the best of Roman architectural genius, but also technological marvels lost for thousands of years. After the collapse of Rome, almost the knowledge of its construction was lost. It took over a thousand years for civilization to rediscover even half of it.
Here's a watercolor, created from outlines made by a public-domain DXF 3D model.
During the Dark Ages, many architects tried to build cathedrals with similar wide spans, but they required buttresses (and later, flying buttresses) to prevent the side walls from bulging out and collapsing.
How did the Roman's accomplish it? This cross section illustrates how:
The Romans constructed the ceiling's vaulted dome as if the building contained a perfect sphere, and they used the same continuous-pouring technique for the concrete as for the Hoover Dam (a technique only fully mastered again 1800 years later). Because the building is virtually built as a single piece of stone, it's actually the floor which is holding the ceiling together and stopping the walls from bulging out.
The first architect who actually bettered the Pantheon design was probably Michelangelo, who achieved a higher dome by putting iron chains around the circumference of the roof. That was the Baslica Dome, built for the Pope in 1626 AD.
Later architect's found a way to make the dome appear taller than it actually is, by gradually decreasing the size of the dome's inner panels higher up. Here's an example from England (can you guess where?).