When we talk about the "ancient Greeks," we really mean the "ancient Athenians." Scratch the surface of the Hellenic ideal, and it's almost always classical Athens of the fifth and fourth centuries BC that you find lying underneath: the architecture of the Parthenon, the philosophy of Plato and Aristotle, the "invention" of democracy, the tragic drama of Aeschylus, Sophocles and Euripides. Occasionally Athens' great rival and antitype gets a look: Sparta, with all its anti-intellectualism, its unbending social hierarchy, its rigid--and, for a time hugely successful--militarism. (In fact, up until the middle of the last century, Sparta was, for obvious reasons, a much firmer favorite with the European elites than the dangerously radical, democratic Athens.) And if you move a little later to the third and second centuries BC, there is the huge Greek city of Alexandria too--founded on the Nile delta by Alexander the Great, home of the greatest library of the ancient world and a busy school of literary production that almost rivaled classical Athens.
But of the hundreds of small independent city-states that made up the "ancient Greeks" of the classical period (before, that is, Philip of Macedon and his son Alexander gobbled up their independence into the first version of world empire), we know very little indeed. Athenian literature (combined with few surviving documents mostly inscribed on stone) gives us a faint impression of their sheer variety: some almost as democratic as Athens; others about as ingeniously oppressive as Sparta; still others happily, or unhappily, making do with their old kings and aristocrats, apparently unaware of all the political revolutions round about; some (like Corinth) close to the vanguard of art and fashion; others quaint little backwaters. We know so little about any one of these that we could never write their "history" (unless it were to be about 90% fantasy). The safest course when dealing with the "ancient Greeks" has always been to shut your eyes and dream of Athens.
Of course, the Athenians quite literally wrote themselves into history. Thucydides, the 5th century Athenian historian (and general) described and analyzed what he claimed was the greatest war the world had ever known--the Peloponnesian War between Athens and Sparta, which lasted on and off from 431 to 404 BC. It was a self-fulfilling prophecy. In writing about the Peloponnesian War, he made it the greatest conflict ever (and the only classical Greek war whose narrative we can even begin to reconstruct in any detail--apart from the Greco-Persian wars of the earlier 5th century recounted by the historian Herodotus). Likewise, in terms of political comment, theory, pamphleteering and satire, the Athenian drive to write the politics of their city had the inevitable effect of making their political arrangements (and especially their democracy, which in its most radical form was actually relatively short-lived and bitterly contested) one of the most important models for future generations.
Predictably too, later Greeks (as well as the Romans, who were the effective masters of the Greek world from the end of the 2nd century BC) were drawn to write and rewrite the history of Athens. Much of our "information" about classical Athens comes from this later process of rewriting. So, for example, the main "source" for the life of Pericles, who was (or so many would claim) the greatest Athenian statesman of the 5th century BC, is a biography written more than five centuries later by Plutarch, a Greek living in the Roman Empire. It is not "just" a biography, of course, but part of a much wider, and much more agenda-ridden, cultural and historical project: to define a place for Greece in a world where Roman domination was the brute political reality. It is, in other words, biography with a very strong ulterior motive. Typically, like most of Plutarch's "Lives," the biography of Pericles is paired with that of a Roman--in this case Fabius Maximus, who successfully masterminded Rome's campaign against Hannibal. Part of the reader's game is to compare life with life: Which do you prefer, the Greek or the Roman? And on what grounds?
Athenian history, even as it was being written in the ancient world, was a complicated palimpsest; version upon version, each one rewritten in new circumstances, in the light of a new political and cultural agenda. Far from being an irritant ("Why don't we just have a simple story?"), these layers of history-writing are among the things that give modern classical studies its distinctively modern tone. There are, and can be, no "flesh and blood" characters in the classical world, no simple stories, only a series of different and competing representations. Ancient history is, and must be, a history of representation; nothing, in fact, could be more postmodern.