Many who attempt to wrest greater truths from the arcane and obscure have often embraced the biblical mention of the Nephilim, transcribing the word as meaning "giants". Frequently, this to support theories that giants once walked the earth, giving credence to apocryphal finds of giant human-like bones. Some use it to bolster their premise in the existence of statuesque hirsute hominids unknown to science.
Then there are those who posit the Nephilim were hybrids, spawned by alien encounters with human women. This belief stems from what is written in Genesis 6:4
When men began to multiply on the earth, and daughters were born to them, the Sons of God saw the daughters of men were attractive. They took as their wives any they chose. The lord said, "My Spirit shall not abide in man forever, for he is flesh: his days shall be 120 years." The Nephilim were on the earth in those days, and also afterward, when the Sons of God came in to the daughters of man and they bore children to them. These were the mighty men who were of old, the men of renown.
But if you re-read that (paying careful attention to the parenthetical notes below), you will see what I do: that the Nephilim are separate from the offspring born from the Sons of God and the women of man. It is these offspring that are the men of old, the men of renown. Not the Nephilim. This section simply states, perhaps as a way to reference WHEN this occurred, that these events took place in the time of the Nephilim.
When men began to multiply on the earth, and daughters were born to them, the Sons of God (meaning not sons of man) saw the daughters of men were attractive They took as their wives any they chose. The lord said, "My Spirit shall not abide in man forever, for he is flesh: his days shall be 120 years." The NEPHILIM were on the earth in those days (meaning the Nephilim were around when this was taking place), and also afterward, when the Sons of God came in to the daughters of man and they bore children to them. These were the mighty men who were of old, the men of renown.
While some scholars do translate the word Nephilim as meaning "giant", many more believe it means either "the fallen" or "those who caused others to fall". They might have been great warriors of old. Ezekiel 32:27 mentions "the mighty fallen," which translates fallen as nophlim.
The reference to a giant is not explicit, but it is metaphorical in Numbers 13:33 when an analog establishes that as we view grasshoppers, so the Nephilim view us. This could be taken to mean that they literally look down on us because they are so tall, but would they really be of comparable to a human/grasshopper height relationship? That seems rather extreme. They would be the size of a 15 story building. It's hard to swallow. But then a lot is, I suppose. Inarguably, the description does come from men that Caleb had sent ahead to scout out the land. When they returned, they spread calumnies (false statements) about the area ahead, saying it was peopled by the Anakites (half-breed giants who some claim were the offspring of human woman and the Nephilim; others believe they were just a group of tall, powerful men) who were much stronger than the Israelites. Since Caleb had been sent by Moses to find the promised land of Milk and Honey, it is curious as to what Caleb's men found that made them want to lie about the land ahead. Perhaps they saw a foe they couldn't defeat and so exaggerated the peril they faced in order to dissuade their fellow Israelites from forging ahead with God's commandment to take the land from them. Perhaps it only means that they saw the Israelites as inferior, insignificant, or pests. Either way, they didn't want to be there.
Going back to Genesis, 'the ones who have fallen' seems most apt if you consider the next section of that book deals with God deciding he didn't like his creation (man? the hybrids?) and was getting ready to flood them out. The Nephilim could be a term applied to them post-deluge when none could quite remember what they called themselves. So, they became the fallen. Those that didn't make it.
Who were they then? It's hard to say. But the bigger question would be... Who were the Sons of God that interbred with human women. It would seem, by context, that it was THIS experiment that needed to be expunged as God then goes on to rinse that gray right outta the earth.
Some theological theorists believe they were the offspring of angels. Angels that come from the heavens, so you could see the intergalactic impregnation theory holding up through that one--even if the sire has shifted from the misconstrued Nephilim to the Sons of God. There is mention in the Bible of 'fallen angels'. Given that Nephilim is likely to mean fallen and Sons of God is a plausible metaphor for Angels, we could easily see this as being the case. And there is linguistic evidence in the bible that correlates the Hebrew phrase for "sons of god" with a section of the Book of Job that specifically talks about angels.
Interestingly, Jewish tradition translates this as "Sons of Nobles," meaning they were completely human, but of a higher social status.
Others believe it references the Sons of Seth, some the Sons of Cain. The list goes on. Aramaic culture, for instance, translates this as the "offspring of Orion," as in the constellation Orion.
So the enigma and controversy will likely continue and it is doubtful we will ever come to understand who exactly were the Nephilim and who these Sons of God must have been.