Genesis 6:1-4 refers to the sons of God and the daughters of men. There have been several suggestions as to who the sons of God were and why the children they had with daughters of men grew into a race of giants (that is what the word Nephilim seems to indicate).
The three primary views on the identity of the sons of God are 1) they were fallen angels, 2) they were powerful human rulers, or 3) they were godly descendants of Seth intermarrying with wicked descendants of Cain. Giving weight to the first theory is the fact that in the Old Testament the phrase “sons of God” always refers to angels (Job 1:6; 2:1; 38:7). A potential problem with this is in Matthew 22:30, which indicates that angels do not marry. The Bible gives us no reason to believe that angels have a gender or are able to reproduce. The other two views do not present this problem.
The weakness of views 2) and 3) is that ordinary human males marrying ordinary human females does not account for why the offspring were “giants” or “heroes of old, men of renown.” Further, why would God decide to bring the flood on the earth (Genesis 6:5-7) when God had never forbidden powerful human males or descendants of Seth to marry ordinary human females or descendants of Cain? The oncoming judgment of Genesis 6:5-7 is linked to what took place in Genesis 6:1-4. Only the obscene, perverse marriage of fallen angels with human females would seem to justify such a harsh judgment.
As previously noted, the weakness of the first view is that Matthew 22:30 declares, “At the resurrection people will neither marry nor be given in marriage; they will be like the angels in heaven.” However, the text does not say “angels are not able to marry.” Rather, it indicates only that angels do not marry. Second, Matthew 22:30 is referring to the “angels in heaven.” It is not referring to fallen angels, who do not care about God’s created order and actively seek ways to disrupt God’s plan. The fact that God’s holy angels do not marry or engage in sexual relations does not mean the same is true of Satan and his demons.
View 1) is the most likely position. Yes, it is an interesting “contradiction” to say that angels are sexless and then to say that the “sons of God” were fallen angels who procreated with human females. However, while angels are spiritual beings (Hebrews 1:14), they can appear in human, physical form (Mark 16:5). The men of Sodom and Gomorrah wanted to have sex with the two angels who were with Lot (Genesis 19:1-5). It is plausible that angels are capable of taking on human form, even to the point of replicating human sexuality and possibly even reproduction. Why do the fallen angels not do this more often? It seems that God imprisoned the fallen angels who committed this evil sin, so that the other fallen angels would not do the same (as described in Jude 6). Earlier Hebrew interpreters and apocryphal and pseudopigraphal writings are unanimous in holding to the view that fallen angels are the “sons of God” mentioned in Genesis 6:1-4. This by no means closes the debate. However, the view that Genesis 6:1-4 involves fallen angels mating with human females has a strong contextual, grammatical, and historical basis.