The progeny of the fallen angels with the daughters of Adam (see notes on Gen. 6, and Ap. 23) are called in Gen. 6, Ne-phil-im, which means fallen ones (from naphal, to fall).  What these beings were can be gathered only from Scripture.  They were evidently great in size, as well as great in wickedness.  They were superhuman, abnormal beings; and their destruction was necessary for the preservation of the human race, and for the faithfulness of Jehovah's Word (Gen. 3:15).

This was why the Flood was brought "upon the world of the ungodly" (2Pet. 2:5) as prophesied by Enoch (Jude 14).

But we read of the Nephilim again in Num. 13:33 :  "there we saw the Nephilim, the sons of Anak, which come of the Nephilim".  How, it may be asked, could this be, if they were all destroyed in the Flood?  The answer is contained in Gen. 6:4, where we read :  "There were Nephilim in the earth in those days (i.e. in the days of Noah); and also AFTER THAT, when the sons of God came in unto the daughters of men, and they bare children to them, the same became [the] mighty men (Heb. gibbor, the heroes) which were of old, men of renown" (lit. men of the name, i.e. who got a name and were renowned for their ungodliness).

So that "after that", i.e. after the Flood, there was a second irruption of these fallen angels, evidently smaller in number and more limited in area, for they were for the most part confined to Canaan, and were in fact known as "the nations of Canaan".  It was for the destruction of these, that the sword of Israel was necessary, as the Flood had been before.

As to the date of this second irruption, it was evidently soon after it became known that the seed was to come through Abraham; for, when he came out from Haran (Gen. 12:6) and entered Canaan, the significant fact is stated :  "The Canaanite was then (i.e. already) in the land."  And in Gen. 14:5 they were already known as "Raphain" and Emim", and had established themselves at Asteroth Karnaim and Shaven Kiriathaim.

In ch. 15:18-21 they are enumerated and named among Canaanite Peoples :  "Kenites, and the Kenizzites, and the Kadmonites, and the Hittites, and the Perizzites, and the Rephaims, and the Amorites, and the Girgashites, and the Jebusites" (Gen. 15:19-21; cp. Ex. 3:8, 17; 23:23.  Deut. 7; 20:17.  Josh. 12:8).

These were to be cut off, and driven out, and utterly destroyed (Deut. 20:17.  Josh. 3:10).  But Israel failed in this (Josh. 13:13; 15:63; 16:10; 17:18.  Judg. 1:19, 20, 28, 29, 30-36; 2:1-5; 3:1-7); and we known not how many got away to other countries to escape the general destruction.  If this were recognized it would go far to solve many problems connected with Anthropology.

As to their other names, they were called Anakim, from on Anak which came of the Nephilim (Num. 13:23), and Rephaim, from Rapha, another notable one among them.

From Deut. 2:10, they were known by some as Emim, and Horim, and Zamzummim (v. 20, 21) and Avim, &c.

As Rephaim they were well known, and are often mentioned :  but, unfortunately, instead of this, their proper name, being preserved, it is variously translated as "dead", "deceased", or "giants".  These Rephaim are to have no resurrection.  This fact is stated in Isa. 26:14 (where the proper name is rendered "deceased," and v. 19, where it is rendered "the dead").

It is rendered "dead" seven times (Job 26:5.  Ps. 88:10.  Prov. 2:18; 9:18; 21:16.  Isa. 14:8; 26:19).

It is rendered "deceased" in Isa. 26:14.

It is retained as a proper name "Rephaim" ten times (two being in the margin).  Gen. 14:5; 15:20.  Josh. 12:15 (marg.).  2Sam. 5:18, 22; 23:13.  1Chron. 11:15; 14:9; 20:4 (marg.).  Isa. 17:5.

In all other places it is rendered "giants", Gen. 6:4; Num. 23:33, where it is Nephilim; and Job 16:14, where it is gibbor (Ap. 14. iv).

By reading all these passages the Bible student may know all that can be known about these beings.

It is certain that the second irruption took place before Gen. 14, for there the Rephaim were mixed up with the five nations or peoples, which included Sodom and Gomorrha, and were defeated by the four kings under Chedorlaomer.  Their principal locality was evidently "Ashtaroth Karnaim"; while the Emim were in the plain of Kiriathaim (Gen. 14:5).

Anak was a noted descendant of the Nephilim; and Rapha was another, giving their names respectively to different clans.  Anak's father was Arba, the original builder of Hebron (Gen. 35:27.  Josh. 15:13; 21:11); and this Palestine branch of the Anakim was not called Arbahim after him, but Anakim after Anak.  They were great, mighty, and tall (Deut. 2:10, 11, 21, 22, 23; 9:2), evidently inspiring the ten spies with great fear (Num. 13:33).  Og king of Bashan is described in Deut. 3:11.

Their strength is seen in "the giant cities of Bashan" to-day; and we know not how far they may have been utilized by Egypt in the construction of buildings, which is still an unsolved problem.

Arba was rebuilt by the Khabiri or confederates seven years before Zoan was built by the Egyptian Pharoahs of the nineteenth dynasty.  See note on Num. 13:22.

If these Nephilim, and their branch of Rephaim, were associated with Egypt, we have an explanation of the problem which has for ages perplexed all engineers, as to how those huge stones and monuments were brought together.  Why not in Egypt as well as in "the giant cities of Bashan" which exist, as such, to this day?

Moreover, we have in these mighty men, the "men of renown," the explanation of the origin of the Greek mythology.  That mythology was no mere invention of the human brain, but it grew out of the traditions, and memories, and legends of the doings of that mighty race of beings; and was gradually evolved out of the "heroes" of Gen. 6:4.  The fact that they were supernatural in their origin formed an easy step to their being regarded as the demi-gods of the Greeks.

Thus the Babylonian "Creation Tablets", the Egyptian "Book of the dead", the Greek mythology, and heathen Cosmogonies, which by some are set on an equality with Scripture, or by others adduced in support of it, are all the corruption and perversion of primitive truths, distorted in proportion as their origin was forgotten, and their memories faded away. http://www.edburrell.com/The_Nephilim2.html