The Nephilim: Definitions, History, Identity
Who were the Nephilim? The Nephilim were living beings who allegedly existed in the 5th century B.C. Their origin and nature is mysterious and can be controversial. Some believe the Nephilim were the children produced by the relationship between "the sons of God" and "the daughter of men" (more below), while others aren't convinced that the Bible teaches that. Furthermore, some ancient and modern interpretations associate the Nephilim with a race of giants, while other associate them with fallen angels.
What is the main source for the story of the Nephilim? What is known about the Nephilim is found in the Bible; Genesis 6:1-4 mention the Nephilim (see text below) in a passage that occurs contextually after the story of Cain and Abel, and just prior to the flood that takes place in the lifetime of Noah.
What does the word "Nephilim" mean? Interpreters are divided over the etymology (i.e. the origin) of the word and, therefore, there is not uniform agreement as to the identity of the Nephilim. There are two main views about the word: (1) it describes a physical nature, and conveys that these living beings are giants, or (2) it describes a spiritual nature, and conveys that these living beings are morally corrupt creatures, sinister in nature, and have rebelled against God.
Is there support for believing that the Nephilim were giants? Yes. The Greek translation of the Hebrew Bible (i.e. the Christian "Old Testament"), called the Septuagint, written two centuries before Jesus Christ, translated the Hebrew word "nephilim" as "giants" as do other ancient translations that followed it, like the Latin Vulgate. More recently, the Brown-Driver-Briggs Lexicon of biblical words, while admitting that the etymology of "nephilim" is uncertain, states that the word means "giants".
Is there support for believing that the Nephilim were fallen angels? Yes. A widely-held view in history is that "nephilim" is derived from the Hebrew root word n-ph-l, meaning "fallen"; and if "fallen" conveys a spiritual condition, then some have suggested that a word like "apostate" (i.e. a spiritual defector) is an accurate translation; and if these apostates refer to former angels in heaven, then the nephilim are fallen angels or demons. (more on this theory below)
How do English Bible translations render the word? The word is variously translated by modern-day English Bible translations: King James Version (KJV) - "There were giants in the earth in those days," New International Version (NIV) - "The Nephilim," New Living Translation (NLT) - "giant Nephilites," English Standard Version (ESV) - "The Nephilim," New American Standard Bible (NASB) - "The Nephilim"; the passage reads:
Genesis 6:1-4, "When man began to multiply on the face of the land and daughters were born to them,  the sons of God saw that the daughters of man were attractive. And they took as their wives any they chose.  Then 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" (ESV).
Who were "the sons of God" and "the daughters of men"?
Would identifying the "sons of God" (v. 2) help to identify the Nephilim? The answer to this question is heavily debated, because the relationship between the sons of God and the Nephilim is heavily debated. The question is: Are the Nephilim the offspring of the sons of God and the daughters of men, or not?
Are the sons of God heavenly beings? Some believe they are, positing that fallen angels has intercourse with "the daughters of men". The daughters of men in this view are simply human women. In support of this view, the same Hebrew phrase translated "sons of God" in Genesis 6:2 is rendered "angels of God" in Job 1:6 and 2:1, in nearly all English translations.The result of this spirit-human relationship was a race of "superhumans," which God then destroyed in the flood. This view can be found in the early church (e.g. Tertullian, 2nd century). Some proponents of this view find support in Jude 6-7 and 2 Peter 2:4-6,
Jude 1:6-7, "And the angels who did not stay within their own position of authority, but left their proper dwelling, he has kept in eternal chains under gloomy darkness until the judgment of the great day— just as Sodom and Gomorrah and the surrounding cities, which likewise indulged in sexual immorality and pursued unnatural desire, serve as an example by undergoing a punishment of eternal fire" (ESV)
2 Peter 2:4-6, "For if God did not spare angels when they sinned, but cast them into hell and committed them to chains of gloomy darkness to be kept until the judgment;  if he did not spare the ancient world, but preserved Noah, a herald of righteousness, with seven others, when he brought a flood upon the world of the ungodly;  if by turning the cities of Sodom and Gomorrah to ashes he condemned them to extinction, making them an example of what is going to happen to the ungodly" (ESV).
In response, some Christians have noted that Christ taught that angels do not marry (cf. Matthew 22:30), which they see as contrary to this interpretation.
Are the sons of God descendents of Seth? Some believe they are of the line of Seth, the third son of Adam and Eve. This position argues that the evil (cf. Gen. 6:5), which led to the flood, was that the wicked line of Cain, called "the daughters of men," overcame the Godly line, called "the sons of God." Proponents of this view find support in Christ's statement that before the flood people were marrying and giving in marriage (cf. Matt. 24:38). In response to this view, it has been suggested that there is nothing in the context of Genesis 6 to warrant identifying the daughters of men with Cain or the sons of God with Seth.
Are the sons of God ancient kings? Some believe they are, perhaps from the line Lamech, who married many women as a demonstration of their power. These are "the men of renown" (cf. 6:4).
Other passages that mention the nephilim
Does Numbers 13:33 refer to the Nephilim? The verse reads, "And there we saw the Nephilim (the sons of Anak, who come from the Nephilim), and we seemed to ourselves like grasshoppers, and so we seemed to them" (ESV). Some interpreters believe that this is a reference to the offspring of the Nephilim who are mentioned in Genesis 6:4. Others respond that Genesis chapters 6-9 imply that those Nephilim didn't survive the flood, because only Noah's family did. It is suggested that the characters in the Numbers narrative call the Canaanite people "nephilim" to simply communicate their unusually large physical stature, and they aren't attempting to identify them with the pre-flood living beings.
Does Ezekiel 32:27 refer to the Nephilim? The verse reads, "And they do not lie with the mighty, the fallen from among the uncircumcised, who went down to Shell with their weapons of war, whose swords were laid under their heads, and whose iniquities are upon their bones; for the terror of the mighty men was in the land of the living." The word translated "fallen" comes from the Hebrew word "no-fly," a variation of which is "nephilim." In context, however, the word in Ezekiel refers to dead Philistine warriors.
1. New Bible Commentary, Carson, D.A. (ed.)
2. Bible (various editions and translations)
3. Wikipedia, "leviathan"