Forget the Übermensch, the Last Man and the Eternal Return, if Nietzsche really did have a determining influence on 20th century intellectual thought it was through his idea of the historical reinterpretation of reality:
“There is no set of maxims more important for an historian than this: that the actual causes of a thing’s origin and its eventual uses, the manner of its incorporation into a system of purposes, are worlds apart; that everything that exists, no matter what its origin, is periodically reinterpreted by those in power in terms of fresh intentions; that all processes in the organic world are processes of outstripping and overcoming; and that, in turn, all outstripping and overcoming means reinterpretation, rearrangement, in the course of which the earlier meaning and purpose are necessarily either obscured or lost. No matter how well we understand the utility of a certain physiological organ (or a legal institution, a custom, a political convention, an artistic genre, a cultic trait) we do not thereby understand anything of its origin.”
Suddenly everything we know becomes suspicious. The accounts we have been given are no longer reliable, in fact they are almost certainly smoke-screens erected to hide the truth. And then comes the realisation that – if everything we know has come from distractions, deliberate lies even, then what do we know? Here we see the best of Nietzsche’s scepticism and cynicism. Like Diogenes, some two thousand years before him, he was looking at the Emperor, saw that he was naked and proclaimed the truth.
From Nietzsche onwards history “becomes a continuous chain of reinterpretations and rearrangements, which need not be casually connected among themselves.” Evolution “is a sequence of more or less profound, more or less independent processes of appropriation… as well as the results of successful counterattacks.”
The observations are brilliant, but Nietzsche himself does not conclude a subsequent need to discover and unveil the truth from this constant chain of falsities and falsifications, rather he applauds the falsifications as necessary (without using the actual term) and imagines his Will to Power exploiting this condition in which progress “is measured by all that must be sacrificed for its sake”, coming to the proto-fascist conclusion that: “To sacrifice humanity as mass to the welfare of a single strong human species would indeed constitute progress…” Unfortunately, there could not be a more perfect Nazi slogan.
Nietzsche, who saw the great dangers of nihilism and was terrified by them, just as he was terrified by the negating process of scepticism, needed an anchor for his thought, an anti-nihilistic grounding, for he knew that without one humanity was doomed. The will to power was one of those anchors, as was the Eternal Return. While the latter was indefinite, fantastical and weak, the former was perverse, only succeeding in dragging his most brilliant sun-scorched illuminations into the cool shade of the status quo. His idea of power as freedom would prove to be deeply reactionary and after Nietzsche the 20th century produced a succession of power/freedom regimes that have made humanity more insipid and ignoble than ever before. We now have a power/freedom aristocracy that is driving humanity to the brink of destruction and Nietzsche’s dreams of sacrifice for the good of the single strong species seem hardly any different to Christian fantasies of the Apocalypse.
 Friedrich Nietzsche, THE GENEALOGY OF MORALS, 2nd Essay, XII