So we've all seen maps of ancient empires. Anyone who dips their toes into classical history probably has a rough idea of the general "shape" of the Roman Empire for example (at least, the fleeting territorial peak under Trajan). What always bugs me when I look at these "maps" of ancient Empires is the question of how exactly historians settled on where to literally draw the line.

The most egregious examples I have come across are things like this showing the ancient Middle East between the fall of the Neo-Assyrian Empire and the Rise of the Achaemenids, or this monstrosity from Wikipedia. (The Assyrian Empire in particular seems to arbitrarily gain and lose vast swathes of territory from one map to the next, at least maps of the Roman and Persian Empires are somewhat consistent.)

How on earth can we know the exact boundaries of the Median Empire to such a degree of accuracy? Why were they given huge amounts of Iran but not that one sliver of Northern Anatolia? How do we establish the border with the Babylonian Empire? Not to mention the straight line across Arabia in the Assyrian Empire map.

Is there any way to know with a reasonable degree of accuracy where the territory of one ancient Empire began and another ended? Did such concepts as defined borders even exist in the ancient world (beyond obvious natural geographic boundaries like rivers and mountain ranges)? If not, how then do/did historians settle on approximations that we see on modern maps of these bygone political entities?