We had a thread on this a while back, but I'll summarize what the Church Fathers have said + theories on how this applies to our day.  The Church Fathers are not unanimous on what Scripture means when it says "giants".  The book of Enoch (which the Jєωs considered as Canon for centuries, even in Christ's day, since Christ refers to this book a few times) explains what the giants were - namely, that demonic spirits had children with earthly women using witchcraft.  Many Church Fathers believed this to be true and wrote about it extensively.
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If this is true, then this explains how we get the "spirits which roam the earth" because they are the souls of the giants, who after they died, lost their human bodies but their spirits remained, until the end of the world, where they will go to hell.  These spirits are not to be confused with the evil angels, since they are pure beings, while the giants were part human/part angel.  I'm not an expert but it seems to me that there is a difference between the bad angels whom St Michael drove to hell who rebelled against God (whom we call devils) and those fallen angels in Genesis whom we refer to as "evil spirits" who still roam earth and try to corrupt humanity.  The difference makes sense to me.  It explains how and why there are some "evil spirits" on earth and some "devils in hell".  
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However, around the time of St Augustine, early 400s, when the Church was choosing what books to include in the Scripture, She chose not to include the book of Enoch because at some point between Christ's time and 400 years later, this book had been lost (probably after the romans destroyed the Temple in 70AD, but i'm just guessing).  When it was "re-discovered" there was much debate over its integrity as many thought parts had been re-written.  So it was not made part of the canon of Scripture.  But, this book is still "esteemed".
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At this time of the codifying of Scripture, there was also a change in the understanding/teaching of what certain passages meant.  As I understand it, and as you can read in the Haydock commentary, the term "sons of god" was changed from meaning "angels" (as many, many Church Fathers understood it) to mean the "sons of Shem" (i.e. men who followed God's laws and the true Jєωιѕн religion).  So this term went from being explained as actual angels to meaning holy men.  Thus, the giants were formerly explained as being the offspring of fallen angels and female witches, (which there is a lot of evidence to support this view) and they now were explained as simply being the offspring of former-virtuous men who married female pagans and their offspring were atheist pagans who hated God and the Jєωιѕн law.
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As one commentator put it, at the time of the 400s when the Church was putting together the Bible, it seems that many at that time in the world did not believe in the former fairy-tales of Scripture, or of the ancient folktales of the former great civilizations.  So the idea of angels and giants and such things were scoffed at and were not part of the mindset of this time (much like ours).  So it seems the Church may have sanitized this part of Scripture (being that it's not a doctrinal or theological fact anyway).
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My view is this, based on 1) Anne Catherine Emmerich's commentary, 2) many Church Fathers, 3) and some current day Protestant bible researchers who are re-reading these passages in light of our present day technology and growing paganism and Satanism  (issues which the Church did not have a need to face in the 400s or even the last 2,000 years).
1.  It is interesting to note that the giants came into being right at the beginning of the world, in Genesis, after the Redeemer is promised to Adam and Eve.
2.  The devil knew that the redeemer would be born of a woman and he would be both God and man.
3.  Therefore, if we take the early Church Father's (and Old Testament Jєω's) understanding of Genesis to mean that ACTUAL fallen angels had children with earthly women, which resulted in giants being born, this makes sense because...

4.  (Theory) The devil was trying to corrupt human nature by polluting human genetics with the spiritual poison of Satanism.  Because if satan could corrupt human nature, and rid the world of all those who were 100% human, then the Redeemer could not be born.  Because how could God be 100% man if all men were part (even 1%) fallen angel?
5.  Ok, ok, this is a crazy theory, right?  Well, let's look at what Genesis says right before God sent the flood to destroy mankind.
6.  "Noe was a just and perfect man in his generations, he walked with God." (Gen 6:9)

7.  Ok, so we know that "just" means that Noe was a holy man, but what does "perfect in his generations" mean, if not related to his perfect, human genes (meaning he was not corrupted genetically speaking)?
8.  Verse 11, Scripture says that "the earth was corrupted and filled with iniquity" (Gen 6:11).
9.  Now, we might read "corrupted" to be a synonym for sin, yet then Scripture uses the term "iniquity" which obviously refers to sin.  So then, the word "corruption" does not refer spiritual vice but to the material aspect of humanity.

10.  Next verse says that God saw all the corruption and "for all flesh had corrupted its way upon the earth" and that "the earth is filled with iniquity through them".
11.  (Theory) God said that "all flesh had corrupted its way"...if corruption refers to spiritual sin, how does this make sense, being that animals and plants and all of nature cannot sin, since they have no soul.
12.  Secondly, God said that the earth's iniquity came THROUGH the corruption of the animals/humans of the earth.  Obviously, this "corruption" was not sin because how can sin fill the world with sin?  It makes no sense.  This "corruption" must refer to a corruption of nature, or of genetics - both related to animals and humans.
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Conclusion:  God allowed the fallen angels to come to earth and to "marry" the daughters of Eve, which led to a corruption of most of humanity and eventually of all living things.  The book of Enoch explains how the fallen angels taught mankind about science, magic, sorcery, metallurgy, and chemistry.  The fallen angels taught men how to make weapons, potions, herbal tinctures, machines, etc, etc.  With the length of time that men lived back then (hundreds of years), it is not out of the question to imagine that their civilization was vastly technologically superior to ours and such legends as Atlantis, (which was said to be destroyed by a large flood) show that there is historical evidence for a great tech age in the far past.
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I believe that mankind and animal kind (i.e. all flesh had corrupted it's way) were satanically genetically modified so as to corrupt the world in an attempt by satan to prevent the Redeemer.  Such corruption by the fallen angels led to iniquity of the highest order, led to wars of unimaginable horror, and to a worship of the earth/science and the giants as being "god men".  Is our day, which is filled with all manner of evils, anything new?  As Scripture says, "there is nothing new under the sun."  If we see the possibility of such genetic monstrosities and we see the corruption of the morals through paganism and Satanism, can it not be that such has happened before, to a greater extent?
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Noe was just (i.e. holy) and his generations were perfect (i.e. 100% human).  So his sons were also 100% human.  Were the daughters that his sons married 100% pure?  Scripture does not say they were; we must assume not.  After the Flood, Noe's 3 sons were not all faithful to God and His Commandments.  Shem was the most faithful and his followers became the Chosen People (Shem = shemites, or semites).  Ham's son, Canaan, was the one cursed by Noe and his race turned against God.  Japeth's race did not follow all of God's laws but they were not as evil as Canaan's race.
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So how did giants re-appear on the earth, post flood?  Logically, they came from Ham's wife whose genes were passed onto Canaan, who in his fall from grace turned to Satanism and was able to (try again) to corrupt the world, both genetically and morally.  Looking at the names of peoples who were descendants of Ham/Canaan, you can see many of the peoples who terrorized the Isrealites (i.e. Shem's bloodline):  Canaanites, Hitites, Amorites, Phillistines, and the king Nimrod.
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Interestingly, but not surprisingly, Nimrod was the king who tried to build the one-world religion and government and the Tower of Babel in mockery of God, in Babylon.  Nimrod was a descendent of Ham and the evil Canaan and worshipped the devil.
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This is why you see in the Old Testament that God commanded the Isrealites to conquer all those pagan civilizations and to kill all living human beings, animals, everything.  Because such civilizations were satanic and corrupt to the highest degree.  For example, when God told Joshua to conquer Jericho by marching around the city for 7 times with the Ark of the Covenant, He told the Israelites to destroy the city and everything in it, even the animals:
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(Joshua 6:17)  And let this city be an anathema, and all things that are in it, to the Lord. Let only Rahab the harlot live, with all that are with her in the house: for she hid the messengers whom we sent.
¹⁸ But beware ye lest you touch ought of those things that are forbidden, and you be guilty of transgression, and all the camp of Israel be under sin, and be troubled.
¹⁹ But whatsoever gold or silver there shall be, or vessels of brass and iron, let it be consecrated to the Lord, laid up in his treasures.
²⁰ So all the people making a shout, and the trumpets sounding, when the voice and the sound thundered in the ears of the multitude, the walls forthwith fell down: and every man went up by the place that was over against him: and they took the city,
²¹ And killed all that were in it, man and woman, young and old. The oxen also and the sheep, and the asses, they slew with the edge of the sword.
²² But Josue said to the two men that had been sent for spies: Go into the harlot's house, and bring her out, and all things that are hers, as you assured her by oath.
²³ And the young men went in and brought out Rahab, and her parents, her brethren also and all her goods and her kindred, and made them to stay without the camp.
²⁴ But they burned the city, and all things that were therein; except the gold and silver, and vessels of brass and iron, which they consecrated into the treasury of the Lord.
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Why did God want this city burned to the ground, and all that was in it?  Because Jericho was the first Canaanite city that the Israelites attacked upon entering the land of Canaan.  And why did God want the land of Canaan to be destroyed?  Because it was satanic, and anti-god; filled with corruption of the flesh and of sin, just like in the days before the Flood.
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Thus we can see that, in order to prepare the way for the birth of the Redeemer, God had the Israelites play the part of destroying most of the remnants of the the pre-Flood Satanism on earth.  However, whenever the Isrealites fell into the worship of false gods, then God had these pagan people conquer them, as he did when the Egyptians turned them into slaves.  The story of David vs Goliath is another tale of a holy boy, David, defeating the massive, pagan/satanic Goliath, who was a Philistine and a descendent of Ham.  So we see the age old battle of good vs evil, God's forces vs satan's forces, Catholics vs non-catholics.
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Who is to say that in our day, with the rise of technology, the rise of paganism, the rise of hatred of god, that we do not see the return of some of the pre-flood corruption, in both genetically altered beings:  half human/half animal or half human/half machine or even half human/half demon?  Could the giants be born again on earth, to wrech havoc on Christians and to conquer the world for the anti-Christ?
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Could these stories of aliens from other planets be the explanation for how these giants have come into existence?  How else can they be explained?  These giant/aliens with super-technology, super (demonic) intelligence, who "bring peace" to the world.  Has the US govt been bringing these beings into existence in places like area 51?
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As Christ said about the end times:  And as in the days of Noe, so shall also the coming of the Son of man be.  (Matt 24:33).  Is it really that far-fetched of an idea?