In the Hebrew Bible and several non-canonical Jewish and early Christian writings, nephilim (in Hebrew הנּפלים means The Fallen [ones]) are a people created by the cross-breeding of the "sons of God" (beney ha'elohim, בני האלהים) and the "daughters of men". (See Genesis 6:1.) The word nephilim is loosely translated as giants or titans in some Bibles, and is left untranslated in others. There is some controversy as to the identity of the "sons of God" who fathered them; apparently, the Hebrew authors believed they were angels or minor gods.
Despite the literal text of the Bible, the idea that heavenly beings mated with humans is controversial, particularly among Christians, who cite the teaching of Jesus in the Book of Matthew that angels do not marry. Others who find the idea of angels mating with humans as distasteful have suggested more figurative interpretations of the nephilim, such as the idea that they were the offspring of men possessed by demons, or of aliens.
Still others believe that the most reasonable view of Genesis 6:1 is that the allusion refers to the fact that some men, from the godly lineage of Seth, called “sons of God” (an expression denoting those in covenant relationship with YHWH - cf. Deuteronomy 14:1; 32:5), began to pursue fleshly interests, and so took wives of “the daughters of men,” i.e., those who were unbelievers.
There are two clear Biblical references to the Nephilim, one in the Book of Genesis 6:1-4 as the offspring of "the sons of God" and "the daughters of men", and the other in the Book of Numbers 13:33 as inhabitants of the land of Canaan.
They are mentioned in two contexts in the Bible:
Nephilim in Genesis
- "...Noah fathered Shem, Ham, and Yefeth. Man began to increase on the face of the earth, and daughters were born to them. The sons of God saw that the daughters of man were good, and they took themselves wives from whomever they chose. God said, 'My spirit will not continue to judge man forever, since he is nothing but flesh. His days shall be 120 years.' The nephilim ("giants" or "titans") were on the earth in those days and also later. The sons of God had come to the daughters of man and had fathered them. They were the mightiest ones who ever existed, men of renown."  (Genesis 6:1-4)
Thus from the above source the nephilim are the "sons" of the union between the "sons of God" who are supposedly fallen angels according to classical Judaic explanations (Targum Jonathan)  and the daughters of man descended from Adam.
It is sometimes suggested that ridding the Earth of this race of giants was God's real purpose in flooding the Earth in Noah's time.
Nephilim in Numbers
- "God spoke to Moses, saying: 'Send out men for yourself to explore the Canaanite territory that I am about to give the Israelites...The men headed north and explored the land...They gave the following report:'...However, the people living in the land are aggressive, and the cities are large and well fortified. We also saw "the giant's" (ha'anak) descendants there'...They began to speak badly about the land that they had explored. They told the Israelites: 'The land that we crossed to explore is a land that consumes its inhabitants. All the men we saw there were "huge men" (anshei midot). While we were there, we saw the nephilim ("giants" or "titans"), they were sons of the "giant" (anak), who descended from the nephilim ("giants" or "titans"), and we saw ourselves as tiny grasshoppers and that's what we were in their eyes."  (Numbers 13:1-2;21;27-33).
From the above episode in the Book of Numbers it is therefore the spies sent by Moses to scout out the land who give negative and frightening descriptions about the land of Canaan and who provide reports of the nephilim inhabiting the land. From the context of that report it is clear that they assume that their listeners already know about the nephilim whose origins are described in the Book of Genesis.
Anakim and the Rephaim
The Anakim and the Rephaim, which are mentioned in the books of Deuteronomy and Joshua, are races of giants which descended from the Nephilim.
Rephaim - lofty men; giants, (Gen. 14:5; 2 Sam. 21:16, 18, marg. A.V.,
Rapha, marg. R.V., Raphah; Deut. 3:13, R.V.; A.V., "giants").
The aborigines of Palestine, afterwards conquered and
dispossessed by the Canaanite tribes, are classed under this
general title. They were known to the Moabites as Emim, i.e.,
"fearful", (Deut. 2:11), and to the Ammonites as Zamzummim. Some of them found refuge among the Philistines, and were still existing in the days of David. We know nothing of their origin.
See also : Valley of Rephaim
The Anakim are the descendants of Anak (Josh. 11:21; Num. 13:33; Deut. 9:2).
They dwelt in the south of Palestine, in the neighbourhood of
Hebron (Gen. 23:2; Josh. 15:13). In the days of Abraham (Gen.
14:5, 6) they inhabited the region afterwards known as Edom and
Moab, east of the Jordan river. They were probably a remnant of the original inhabitants of Palestine before the Canaanites, a Cushite tribe from Babel, and of the same race as the
Phoenicians and the Egyptian shepherd kings . Their formidable
warlike appearance, as described by the spies sent to search the
land, filled the Israelites with terror. They seem to have
identified them with the Nephilim, the "giants" (Gen. 6:4; Num.
13:33) of the antediluvian age. There were various tribes of
Anakim (Josh. 15:14). Joshua finally expelled them from the
land, excepting a remnant that found a refuge in the cities of
Gaza, Gath, and Ashdod (Josh. 11:22). The Philistine giants whom David encountered (2 Sam. 21:15-22) were descendants of the Anakim.
Nephilim in other works
The story of the Nephilim is chronicled more fully in the Book of Enoch (part of Ethiopian biblical canon).
There are also allusions to these descendants in the deuterocanonical books of Judith, Sirach, Baruch, and Wisdom of Salomon.
Cultural references to Nephilim
The antediluvian Nephilim are a key plot element in Madeline L'Engle's science fantasy novel Many Waters.
Fields of the Nephilim is the name of a gothic rock group.
The X-Files episode "All Souls" features four dying, disfigured girls that Scully believes are Nephilim.
Nephilim is a role-playing game by Chaosium, in which the players take on the roles of ancient spirits that can move from one human incarnation to another.
The Nephilim are a race of beings from a parallel plane that interact with humans in Gregory Keyes's trilogy Age of Unreason.
Nephilim is the name of a mysterious and little girl in the Xenosaga game series produced by Namco.
In the video game Wing Commander: Prophecy, Nephilim is the code name given to a race of insectoid extraterrestrials who invade our galaxy via an artificial wormhole.
In the video game Diablo 2 the Ancients Ones are referred to as "Spirits of the Nephilim". They guard The Worldstone Keep, which leads to the Throne of Destruction, where Baal, the boss of the game resides. Their names are; Madawc The Guardian, Korlic The Protector, and Talic The Defender.
In Mick Farren's Renquist Quartet, the Nephilim are a race of aliens ruled by a king named Marduk Ra. They conquered Earth in prehistory, and are the basis of all religions. They conducted experiments on primitive humans, creating a warrior race. The Nephilim then left Earth to pursue a war. The abandoned warriors became the basis of vampire legends.
Nobody seems to know what the singular form of "Nephilim" is, Although following the trend of Anak to Anakim, Cherub to Cherubim and Seraph to Seraphim, perhaps "Nephil" might make sense.