Old Testament: Genesis 6:1-7

"When man began to multiply on the face of the land and daughters were born to them,2 the sons of God saw that the daughters of man were attractive. And they took as their wives any they chose. 3 Then the Lord said, “My Spirit shall not abide in[a] man forever, for he is flesh: his days shall be 120 years.” 4 The Nephilim[b] 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.5 The Lord saw that the wickedness of man was great in the earth, and that every intention of the thoughts of his heart was only evil continually. 6 And the Lord regretted that he had made man on the earth, and it grieved him to his heart. 7 So the Lord said, “I will blot out man whom I have created from the face of the land, man and animals and creeping things and birds of the heavens, for I am sorry that I have made them.”

In the movie based on the best-selling novel, Mortal Instruments,
Nephilim: described as angel-human hybrids that hunt demons

My primary question is this: what actually are the Nephilim? There is great debate as to the answer. Some interpretations translate the word to mean "the fallen" as in the angels fallen from Heaven (wikipedia); however, when referred to elsewhere they are classically known as the Gregori, or Watchers, not the Nephilim, such as in the Apocryphal test of the Book of Enoch, which ascribes Heaven with layers more like Hades from Greek mythological legend. (Secrets of Enoch, Ch 18, http://sacred-texts.com/chr/apo/index.htm) Watchers are also mentioned in the apocryphal text of the Book of Jubilees. (4:15 and 5:1) 

Other translations interpret the word Nephilim as giants. This theory is somewhat supported in Numbers 13:32-33; when the twelve spies were sent out, they came back with reports of giants which they referred to as Nephilim. Rather than thinking of the giants as their own race though, it makes more sense to think of these peoples as having giantism, or gigantism. This disorder is rare in modern day society, but in (for lack of a better word) "Bible Times" it seems this condition was fairly common in peoples of a certain descent. (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4113151) Giantism is described as "abnormal growth due to an excess of growth hormone during childhood."  (http://www.nlm.nih.gov/medlineplus/ency/article/001174.htm)

Also "As per modern medical understanding, pituitary gigantism today is caused by a tumor (cancerous growth in) the pituitary gland in the brain, which causes an overproduction of Human Growth Hormone. (1) While some cases of pituitary tumors like this occur randomly, others are genetically linked and pass down through families. (2)" 

(I think this article is interspersed with a bit of weird mysticism about demon spirits and such, but most of the information after the hyperlinked stitchiniswrong.com I believe is fairly accurate.  http://www.nephilimhybrids.com/nephilim-hybrid/modern-nephilim-hybrid-deception-part-2)

 It's also a little known fact that the average Hebrew male stood only about 5 ft 3, maybe up to 5'5" or 5'7" according to some archaelogical digs. Giants to them could have ranged any where from 6 ft (average Canaanite) to 9 (Philistine's Goliath size, discrepancies vary) or possibly even up to 13 ft ( "King Og of Moab, Deut. 3:11 had a bed measuring 9 cubits long and 4 cubits wide (13 ft by 6 ft) [but that does not mean King Og was the same size as his bed. -- E.T.B.]")

(http://etb-pseudoscience.blogspot.com/2012/03/nephalim-giants-in-old-testament.html)

(http://biblestudymagazine.com/interactive/goliath)

Watchers, as portrayed in the 2014 movie Noah (Russell Crowe, Logan Lerman and Emma Watson)
(http://www.suchacritic.com/wp-content/uploads/2014/05/Noah-Watcher-V2-luca-nemolato.jpg)

Yet another theory have the identification of Nephilim that goes back Cain. If we take Nephilim to mean "the fallen" (which many linguists have determined as folly), then this theory fits well, Adam and Eve being the first to "fall" when they ate of the forbidden fruit (Genesis 3:6) and Cain being marked and cursed by God (though protected) when he slew his brother Abel. Seth was born to Adam and Eve later, and Seth was very blessed by God. The sons of God could refer to the descendants of Seth, whereas the daughters of man would refer to descendants of Cain. Although the Nephilim are also mentioned in Numbers. how can they be referring to further descendants of sons of Seth and daughters of Cain if everyone except Noah's immediate family was wiped out in the flood? Noah is a descendant of Seth. Unless Noah and/or his sons had married descendants of Cain, the Nephilim would have died out. Which according to the Apocryphal text of the Book of Jasher is probable. Also, perhaps the Nephilim in Numbers are different from the ones mentioned in Genesis, because the ones mentioned in Numbers 13 are said to be descendants of Anak.

^{32 "}And they spread among the Israelites a bad report about the land they had explored. They said, “The land we explored devours those living in it. All the people we saw there are of great size. ³³ We saw the Nephilim there (the descendants of Anak come from the Nephilim). We seemed like grasshoppers in our own eyes, and we looked the same to them.”

(this article has some bias, but provides some interesting information http://www.douglashamp.com/the-sons-of-seth-and-daughters-of-cain-theory-refuted)

There aren't really a lot of straight answers across the board, but the solution to the mystery of the Nephilim seems to be firmly rooted in the DNA of those Biblical individuals with Giantism. Although if anyone else finds any more information regarding the Nephilim, I would be very interested to look into it.