This post based on a question about angels called into the TCT Network program, Ask The Pastor. People frequently ask the interpretation of Genesis 6:4. I thought I'd tackle it in short.  

The Antediluvian Age

Antediluvian is a word that describes the period before the flood chronicled in Genesis 6-9. This is also the age of man before law. This is alluded to in Romans 2:14:
For when the Gentiles, which have not the law, do by nature the things contained in the law, these, having not the law, are a law unto themselves:
Because man lived without laws, they lived however they chose. And evil seeming more pleasurable than good, man's wickedness increased without restraint.
And GOD saw that the wickedness of man was great in the earth, and that every imagination of the thoughts of his heart was only evil continually. Genesis 6:5

Sons and Daughters of the Earth

And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them, That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose. Genesis 6:1-2
Note here that not all men were evil. Some remembered the lessons learned in the Garden. Adam taught his children about God and the knowledge was passed down for generations. Some, like the sons of Seth,  continued to acknowledge God, while most, like the sons of Cain, walked in the own way. Nevertheless, there was little restraint practiced by any. The sons of God even took wives of as many women as they desired. Now, while this may have kept in practice the commandment to be fruitful and multiply, this was not God's intent. God is a God of order. Man, in this case, went wild and followed their flesh rather than their intelligence.  

So Who Were These Sons of God?

In case it was missed earlier, these are the sons of Seth. There are different thoughts on this taken from the following verse…
There were giants in the earth in those days; 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 mighty men which were of old, men of renown. Genesis 6:4
The word ‘giants' causes a gross misinterpretation. It is believed that these men were literal giants, born from a union of women and angels. Well. there is at least one verse that refutes this thought. First of all, Genesis 6:2 says the sons of God ‘took wives'. Now read this…
For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven. Matthew 22:30
Angels do not marry! Not enough? What about this one?
Thou madest him a little lower than the angels; thou crownedst him with glory and honour, and didst set him over the works of thy hands: Hebrews 2:7
Angels are not organic or natural beings. They cannot procreate! If they could, don't you think God would have allowed them to reproduce with each other instead of creating untold numbers of them?
And I beheld, and I heard the voice of many angels round about the throne and the beasts and the elders: and the number of them was ten thousand times ten thousand, and thousands of thousands; Revelation 5:11 The chariots of God are twenty thousand, even thousands of angels: the Lord is among them, as in Sinai, in the holy place. Psalms 68:17
Can you imagine if Satan could procreate? You think there are evil people in the world now! The movies like Rosemary's Baby and Damien would more reality than fiction! No my dear brothers and sisters. The sons of God were godly men who married the daughters of wicked men. This gave rise to men who became great (giants) and well known (men of renown) Giants is also misinterpreted. Giants in Genesis 6:4 means tyrant or bully. Think about this. We hear of tyrants in countries and bullies in schools today. Imagine the same in a world where evil reigns without restraint. Yes, men with big time chips on their shoulders! These men became ruthless rulers and oppressive lords over people, not 9 feet, 9 inch tall men like Goliath!  

Angels Producing Giants?

If you've read this far, you know I already covered this in the preceding topic. Just to reiterate, angels are not like humans. They cannot procreate. They cannot mate with humans. So giants did not exist because of unions between women and angels. Just think. If that is the case, tall men like Kareem Abdul-Jabbar (7 feet, 2 inches) and Shaquille O'Neal (7 feet, 1 inch) or taller, Robert Pershing Wadlow (8 feet , 11.1 inches) or Sultan Kösen (8 feet, 2.8 inches) would be considered demi-gods!  

Fantasy and Tradition vs Truth

While there were and are giants in our world, they are not the norm. Stories of great men born of natural/supernatural unions are the stuff of movies and mythology. They make for great entertainment, but not biblical truth. Yet many will fight to hold on to such error, even in the face of evidence to the contrary. Why? Man, by nature, desires to be more, to be greater. We are also vain in that we will fight to promulgate error because we, along with countless others, want to believe them. In this case, truth is not what matters. What we choose to believe is true does matter! History as well as scripture teaches us the following: Being a follower of the masses will cost you more than walking side by side with the few.
Enter ye in at the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat: Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it. Matthew 7:13-14
Am I therefore become your enemy, because I tell you the truth? Galatians 4:16