The Nephilim

In Genesis 6:4, it says: "The Nephilim were on the earth in those days—and also afterward—when the sons of God went to the daughters of humans and had children by them. They were the heroes of old, men of renown."

"The sons of God" are often interpreted as fallen angels. This is supported by Job 1:6, where "sons of God" refers to angels: "Now there was a day when the sons of God came to present themselves before the Lord, and Satan also came among them."   

If the above is true, then angels have the ability to produce sperms to impregnate women. In Mark 12:25, it says "For when they rise from the dead, they neither marry nor are given in marriage, but are like angels in heaven."  This strongly indicates that they cannot reproduce. 

Other theories said the Nephilim are powerful kings and nobles. For example, the tallest king every recorded in the scripture was King Og of Bashan. He was the last of Rephaim, a group of giants. In Deuteronomy 3:11, his bed was nine cubits long and four cubits wide, which translates to about 13.5 feet (4.1 meters) long. He is even taller than Goliath, who was six cubits and a span, which is around 9 feet 9 inches (2.97 meters) (1 Samuel 17:4).  If the Rephaim are giant humans, there is a possibility the Nephilim are humans as well.  

The second big question is, why did verse 4 says that the Nephilim exist "afterward".  What does the "afterward" represents? Most people believe that it meant after the flood of Noah. In Genesis 7:21-23 specifically states that "every living thing that moved on land perished—birds, livestock, wild animals, all the creatures that swarm over the earth, and all mankind."  This means all the Nephilim has died during the flood. 

Many theories tried to explain this, including the fallen angels had came back after the flood to impregnate women.  Another theory is that the Nephilim’s traits were carried through Noah’s family, possibly through the wives of his sons.

Another case of Nephilim exist after the flood is from Numbers 13:33 in NIV, where it says "We saw the Nephilim there (the descendants of Anak come from the Nephilim). We seemed like grasshoppers in our own eyes, and we looked the same to them.”

It appears to me that the Nephilim still somehow exist through their descendants, the Anak. This means that the DNA of Nephilim is passed on through Moses' daughter-in-laws.