The Origin of the Nephilim

The nephilim are the offspring formed as the result of fallen angels having sex with human women.

1 When humankind began to multiply on the face of the earth, and daughters were born to them, 2 the sons of God saw that the daughters of humankind were beautiful. Thus they took wives for themselves from any they chose. 3 So the LORD said, "My spirit will not remain in humankind indefinitely, since they are mortal. They will remain for 120 more years."
4 The Nephilim were on the earth in those days (and also after this) when the sons of God were having sexual relations with the daughters of humankind, who gave birth to their children. They were the mighty heroes of old, the famous men.Genesis 6:1-4

The nature of the nephilim depends largely upon the identity of the "sons of God".

The Different Views on the "sons of God"

For more, see the separate article: Who Are the "Sons of God"?

1. Fallen angels
   The oldest and most prominent view is that the sons of God mentioned here are fallen angels who had sex with human women and produced giant offspring called the nephilim. Big-name early supporters include Josephus, Eusebius, Justin Martyr, Tertullian, Irenaeus, and others.
2. Line of Seth
   Augustine, finding the idea of angels having sex with humans repugnant, promoted Julius Africanus' belief that the sons of God were men from the line of Seth--those committed to true worship of God. The "daughters of men," then, were the descendants of Cain. According to this view, God became upset because the Sethites mixed with the Cainites, polluting the line of true worship.
3. Kings and rulers
   The third view is that the sons of God were pre-flood rulers. Rabbi Simeon ben Yochi, in the 2nd century, pronounced a curse on all Jews who adhered to the theory that the sons of God were fallen angels. Rabbis Moshe ben Nachman and Shlomo Yitzchaki helped this third view enter the mainstream.

The sons of God are those born of the Spirit

As noted above, the truth is that the "sons of God" mentioned in Job 38 are, in fact, angels. The phrase itself is not arbitrary or abstract, but has a specific meaning. Only those born directly of God are called "children" or "sons" of God.

What is born of the flesh is flesh, and what is born of the Spirit is spirit.John 3:6

This is why angels are called "sons of God". This is why Adam is called "Adam, the son of God" (Luke 3:38). This is why Christ is called the "Son of God" (Luke 22:70; 8:28, John 3:18; 11:27). This is why Christians are called "children of God"--because they have been "born from above", directly by God (1 Corinthians 5:17, Ephesians 2:10).

Jude

6 You also know that the angels who did not keep within their proper domain but abandoned their own place of residence, he has kept in eternal chains in utter darkness, locked up for the judgment of the great Day. 7 So also Sodom and Gomorrah and the neighboring towns, since they indulged in sexual immorality and pursued unnatural desire in a way similar to these angels, are now displayed as an example by suffering the punishment of eternal fire.Jude 1:6-7

Grk "strange flesh." This phrase has been variously interpreted. It could refer to flesh of another species (such as angels lusting after human flesh). This would aptly describe the sin of the angels, but not easily explain the sin of Sodom and Gomorrah. It could refer to the homosexual practices of the Sodomites, but a difficulty arises from the use of ?te??? ({etero"; "strange," "other"). When this is to be distinguished from ????? (allos, "another") it suggests "another of a different kind." If so, would that properly describe homosexual behavior? In response, the language could easily be compact: "pursued flesh other than what was normally pursued." However, would this find an analogy in the lust of angels (such would imply that angels normally had sexual relations of some sort, but cf. Matt 22:30)? Another alternative is that the focus of the parallel is on the activity of the surrounding cities and the activity of the angels. This is especially plausible since the participles ??p???e?sasa? (ekporneusasai, "having indulged in sexual immorality") and ?pe????sa? (apelqousai, "having pursued") have concord with "cities" (p??e??, poleis), a feminine plural noun, rather than with Sodom and Gomorrah (both masculine nouns). If so, then their sin would not necessarily have to be homosexuality. However, most likely the feminine participles are used because of constructio ad sensum (construction according to sense). That is, since both Sodom and Gomorrah are cities, the feminine is used to imply that all the cities are involved. The connection with angels thus seems to be somewhat loose: Both angels and Sodom and Gomorrah indulged in heinous sexual immorality. Thus, whether the false teachers indulge in homosexual activity is not the point; mere sexual immorality is enough to condemn them.The NET Bible, note on "unnatrual desire" (verse 7)

This verse begins with hos, an adverb of comparison having meanings of "in the same manner as, after the fashion of, as, just as." Here it introduces a comparison showing a likeness between the angels of verse 6 and the cities of Sodom and Gomorrha of this verse. But the likeness between them lies deeper than the fact that both were guilty of committing sin. It extends to the fact that both were guilty of the same identical sin. The punctuation of the A.V. [KJV] is misleading, as an examination of Greek text discloses.

The A.V. punctuation gives the reader the impression that Sodom and Gomorrha committed fornication and that the cities about them committed fornication in like manner to the two cities named. . . . The words "in like manner" are related to the verbal forms, "giving themselves over to fornication" and "going after strange flesh." In addition to all this, the Greek text has toutois, "to these." Thus, the translation should read, "just as Sodom and Gomorrha and the cities about them, in like manner to these, having given themselves over to fornication and having gone after strange flesh." The sense of the entire passage (vv.6, 7) is that the cities of Sodom and Gomorrha and the cities about them, in like manner to these (the angels), have given themselves over to fornication and have gone after strange flesh. That means that the sin of the fallen angels was fornication.Kenneth Wuest, Word Studies in the Greek New Testament, Volume 2, p 241-242

Whichever interpretation you take here, it is clear that Jude is writing about fallen angels having sex with humans. In Jude 1:6 is the Greek word oiketerion, translated "place of residence". The only other time this word is used in the New Testament is in reference to the Christian's resurrection body:

1 For we know that if our earthly house, the tent we live in, is dismantled, we have a building from God, a house not built by human hands, that is eternal in the heavens. 2 For in this earthly house we groan, because we desire to put on our heavenly dwelling...2 Corinthians 5:1-2

This seems to indicate that the fallen angels left their heavenly bodies in order to take human form, which allowed them to have sex with human women.

Etymology

The etymology of nepilim is uncertain, the following explanations have been advanced with mixed reception. First, it may derive from the niphal of the verb pala, meaning "be extraordinary," i.e., "extraordinary men." Second, it may be derived from the verb napal, "fall," in one of the following senses: (1) the "fallen ones" - from heaven, i.e., supernatural beings; (2) morally "fallen men"; (3) "those who fall upon," in the sense of invaders or hostile, violent men; (4) "those who fell by" the sword (cf. Ezk. 32:20f.); (5) "unnaturally begotten men" or bastards (from cf. nepel, "abortion" or "miscarriage").The International Standard Bible Encyclopedia, Volume 3, p 518-519

The Septuagint renders nephilim as gigantes, literally meaning "sons of Gaia" or "earth-born".

Objection - Angels don't marry

Some argue that the "sons of God" in Genesis 6 could not be angels because angels dont' marry.

29 Jesus answered them, "You are deceived, because you don't know the scriptures or the power of God. 30 For in the resurrection they neither marry nor are given in marriage, but are like angels in heaven."Matthew 22:29-30

24 Jesus said to them, "Aren't you deceived for this reason, because you don't know the scriptures or the power of God? 25 For when they rise from the dead, they neither marry nor are given in marriage, but are like angels in heaven."Mark 12:24-25

The problem with this argument is that it confuses the fallen angels spoken of in Genesis 6 with the angels in heaven spoken of in these verses.

Extra-Biblical references

Just like the story of the flood, the idea that angels and humans had sex and produced powerful offspring is almost universal. As such, it is found in many extra-Biblical texts.

Book of Enoch

The Book of Enoch is a collection of writings from the first or second century BC. Though not Scripture, it was held in esteem by both Irenaeus and Clement of Alexandria. Jude even quotes Enoch 1:9 in verses 14 and 15.

1 And it came to pass when the children of men had multiplied that in those days were born unto 2 them beautiful and comely daughters. And the angels, the children of the heaven, saw and lusted after them, and said to one another: 'Come, let us choose us wives from among the children of men 3 and beget us children.' And Semjaza, who was their leader, said unto them: 'I fear ye will not 4 indeed agree to do this deed, and I alone shall have to pay the penalty of a great sin.' And they all answered him and said: 'Let us all swear an oath, and all bind ourselves by mutual imprecations 5 not to abandon this plan but to do this thing.' Then sware they all together and bound themselves 6 by mutual imprecations upon it. And they were in all two hundred; who descended in the days of Jared on the summit of Mount Hermon...Enoch 7:1-6, in The Apocrypha and Pseudepigrapha of the Old Testament, translated by R.H. Charles

1 And Azazel taught men to make swords, and knives, and shields, and breastplates, and made known to them the metals of the earth and the art of working them, and bracelets, and ornaments, and the use of antimony, and the beautifying of the eyelids, and all kinds of costly stones, and all 2 colouring tinctures. And there arose much godlessness, and they committed fornication, and they 3 were led astray, and became corrupt in all their ways. Semjaza taught enchantments, and root-cuttings, Armaros the resolving of enchantments, Baraqijal (taught) astrology, Kokabel the constellations, Ezeqeel the knowledge of the clouds, Araqiel the signs of the earth, Shamsiel the signs of the sun, and Sariel the course of the moon. And as men perished, they cried, and their cry went up to heaven...Enoch 8:1-3, in The Apocrypha and Pseudepigrapha of the Old Testament, translated by R.H. Charles

This tells us that the angels had sex with women, and also that they brought humans advanced weapons technology. Genesis 6:11 tells us that the earth was filled with violence--perhaps this was brought about by the fallen angels' influence.

Book of Jubilees

The Book of Jubilees contains similar content to the Book of Enoch:

1 And it came to pass when the children of men began to multiply on the face of the earth and daughters were born unto them, that the angels of God saw them on a certain year of this jubilee, that they were beautiful to look upon; and they took themselves wives of all whom they 2 chose, and they bare unto them sons and they were giants. And lawlessness increased on the earth and all flesh corrupted its way, alike men and cattle and beasts and birds and everything that walks on the earth--all of them corrupted their ways and their orders, and they began to devour each other, and lawlessness increased on the earth and every imagination of the thoughts of all men 3 (was) thus evil continually...Jubilees 5:1-3, in The Apocrypha and Pseudepigrapha of the Old Testament, translated by R.H. Charles

Jubilees 7:21-25 says that ridding the earth of the nephilim was one of God's purposes for the great flood.

The Book of Enoch and the Book of Jubilees tell the story of the high-ranking angel Samyaza (or Semjaza) leading a sect of rebel angels to Earth to teach humans. After a while, the angels were lusting after the human women and began to teach them things such as magic and conjuring. The rebel angels had sex with the human women, resulting in the nephilim as their offspring. The nephilim are described in these books as being gigantic and strong, having huge appetites, so much so that they resorted to eating humans.

Genesis Apocryphon

The Genesis Apocryphon is a text discovered amongst the Dead Sea Scrolls. It contains a story about Lamech (Noah's father) questioning his wife, believing that Noah was not his son, but rather the result of his wife having sex with either an angel or a nephilim.

Greek mythology

In Greek mythology, the Titans were the children of Uranus (heaven) and Gaea (earth). Cronus (the most famous Titan) killed his father and led a rebellion against Zeus and the gods of Olympus. Defeated, Cronus and the other Titans were cast into Tartarus (the underworld). This reflects the Biblical truth of God destroying the offspring of the angels and humans.

Peter makes an interesting comment regarding the angels and Tartarus:

For if God did not spare the angels who sinned, but threw them into hell and locked them up in chains in utter darkness, to be kept until the judgment...2 Peter 2:4

The Greek for "threw them into hell" is tartarosas. It means "cast them into Tartarus" or "hold them captive in Tartarus".