There are three lines of thought on this:
1. They were angels who took human wives.
2. They were kings exercising the “right of the first night” with any woman who was being given in marriage.
3. They were men from the godly lineage of Seth who took wives from the ungodly lineage of Cain.
Answer one has a magical, mystical appeal to it, but is such a thing even possible? Jesus said that the angels in heaven neither marry, nor are given in marriage (Matthew 22:30). Aree the fallen angels different? Would that mean that they are still capable of mating with human women? This answer appears completely improbable, even impossible.
The second answer has a little more going for it. Kings often claimed to be descended from the gods; the “right of the first night” was still being practised in parts of Europe in Medieval times and goes back to the earliest times (it is mentioned in the Gilgamish Epic). Still, it really isn’t clear that this would have been enough to cause God to destroy the world by a flood.
The third answer seems a better explanation for the fact that by the time of the flood, out of millions of people living at that time, only eight found grace in the eyes of the Lord. The warning given by Moses in Deuteronomy 7:3-4 is meant to avoid a recurrence of this: “Neither shalt thou make marriages with them [the ungodly people of the land of Canaan]; thy daughter thou shalt not give unto his son, nor his daughter shalt thou take unto thy son. For they will turn away thy son from following me, that they may serve other gods: so will the anger of the LORD be kindled against you, and destroy thee suddenly.”
Romans 8:14 states: “For as many as are led by the Spirit of God, they are the sons of God.” Was it any different in the antediluvian world? The sons (and daughters) of God are they who allow God to direct their lives. I see no need to imagine angelic beings in the passage in Genesis 6. Men who were of the godly lineage allowed themselves to be allured by women who did not share their faith in God and the children followed their mothers’ unfaithful lifestyle until only Noah and his family were left.
This is the position taken by most Bible expositors, it was certainly the position of our Anabaptist forefathers. The issue here is not some unearthly commingling of angelic and human persons, but the necessity of purity and a common faith in the marriage relationship.