Who were the "Sons of God" mentioned in Genesis?

Genesis 6:1–4 tells us:

1  —  And it came to pass, when men began to multiply on the face of the earth, and daughters were born unto them,

2  —  That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.

3  —  And the Lord said, My spirit shall not always strive with man, for that he also is flesh: yet his days shall be an hundred and twenty years.

4  —  There were giants (also written Nephilim) 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.

Who were the sons of God mentioned in the Old Testament? Who were the Nephilim?