Q&A: The Nephilim
The Nephilim (“great” or “amazing”) were the first “mighty men” of the Bible. They were the result of the intermarriage between the priestly sons of Seth and the rebellious Cainite kings. The text gives us a split genealogy after the murder of Abel, priests serving God outside the garden, and Cain’s false kingdom (Cain went and built a “fortress” to protect himself). So, humanity was divided into two camps: those who served God as their king and those who rebelled against Him.
The sin of the sons “of God” (God was their authority) was marrying daughters “of men” (man as authority), and we know this is what it is talking about because it happens over and over throughout Bible history. These women were unconverted. Marrying such women was forbidden in the Mosaic Law, especially for kings. This sin eventually brought about Solomon’s apostasy, which destroyed Israel under a Babylonian “flood.” His failure led to a splitting of the kingdom, and Omri in the northern kingdom also attempted to co-op Judah through intermarriage. Ezra and Nehemiah deal with such intermarriage as well. Unconverted women and their children were to be expelled, to save Israel from another judgment.
Finally, Jesus said that His generation would soon be destroyed for such “marrying and giving in marriage,” as it was in the days of Noah. In the first century, the compromisers were the “rulers of the Land,” the Herods and their high priesthood, through their dependance on the state power of Rome. Rather than being an obedient priesthood, humbling themselves and being exalted by God, they exalted themselves and were finally abased.
There is nothing wrong with intermarriage as long as the move is towards God. God loves holy hybrids (just look at some of His angels!) Rahab and Ruth are prime examples. In the first century, this holy intermarriage was the union of Jews and Gentiles in Christ, pictured for many centuries in the Feast of Booths. They too were united, but by the Spirit through priestly obedience. This is true kingdom. Once united, nothing would be withheld from them.
But why were these men in Genesis 6 called “mighty,” the supervillains of the day?
James Jordan has a must-read article on this, aligning the intermarriage with events in our own day.  In summary, what he calls “the Enoch factor” is the habit of the unrighteous initially achieving more, culturally-speaking, than the righteous, because they are willing to resort to slavery and robbery (like Pharaoh, and Rehoboam). But this kind of kingdom is short-lived. It springs up quickly but fades because it has no true integrity. Paganism, left to itself, is unsustainable. The only way paganism can continue is by co-opting the strength and integrity of a righteous culture. This is exactly what has happened in western culture. This is what Jordan calls the “Nephilim factor.” The sanctimonious atheism we see today has no moral capital of its own. It has to borrow, or steal, everything from Christianity, including science, and then relabel this cultural integrity as the product of human reason. What results is a culture of great strength and technical ability, all the blessings of God co-opted, stolen by a corporate Adam. 
The serpent offered Adam a kingdom without priestly obedience first. “You shall be like God.” The Nephilim were simply a race of men who were “like god” (Genesis 3:4-5) in a bad way — “mighty men.” (Notice that David and Boaz were also “mighty men,” but in a good way.) The Nephilim were the fulfilment of this satanic offer, a race of Cains, a sin that was now full grown (as James writes to first century Jews) and ripe for judgment.
So forget the angels, and the aliens. It was the integrity of the Church co-opted and corrupted by a secular state with Messianic pretensions. 
 James B. Jordan, The Case Against Western Civilization.
 See also How To Be Really Evil.
 If the West Wing TV series was renamed “The Messiah Complex,” it would suddenly become the most brilliant satire ever.