Evidence indicates that Judaism of Jesus' era, before, and after, believed that the "sons of God" in Genesis 6 were fallen angels, and that this understanding is also indicated by 1 Peter. Consider the views of this passage:

Sons of God = fallen angels
Support for this is found in the use of the terms "sons of God" for angels in the Bible itself (Job) and in non-Biblical but culturally related texts (from Ugarit, for example, where it is used of lesser deities). This is the earliest known understanding of the text of Genesis (since the 2nd century BC), and was adopted by early Christian writers.

Some reply to this view with the following objections:
1. There is no contextual identification in Genesis 6. This can be readily admitted, but the same applies for any other view of this passage.
2. It is objected that Genesis 6:1-8 concerns humanity and its outcome, not angels and their punishment, but this is a case of assigning a topic arbitrarily and then objecting that another topic does not fit. The lack of reference to angelic punishment is not meaningful; and one may as well say that the subject here is, "humanity -- what happened when fallen angels stepped in".
3. A major objection is that this understanding makes procreation a power of angels, whereas Jesus said that angels do not procreate (Matt. 22:30). However, angels are said to take on human traits, even eating (as they did with Abraham), and one may suggest that fallen angels "used the bodies of ungodly men, by demonic possession, to achieve their evil purpose of producing an evil generation of people." Or, the manipulation of matter may have accomplished a similar purpose. As for Jesus' comment, it is not clear whether this is because angels cannot engage such activity by nature, or are simply forbidden to. Note that Jude 1:6-7 says that angels who "left their habitation" and, like Sodom and Gomorrah, went after "strange flesh", which would suggest that the latter is more likely.

Sons of God = rulers
This was a view of the rabbis and ties in with the reference in Psalm 82 of human rulers as elohim. This does not satisfy contextual requirements either (Gen. 6 does not refer to kingship), and rulers of the period did consider themselves to be divine progeny. But it is hard to see why this should have received any special notice from Genesis.

Sons of God = line of Seth
This view is held by many Christians today and became the dominant interpretation among the Church Fathers, including St. John Chrysostom and St. Ephrem the Syrian. Its positive evidence is:
1. This would relate the text back to the two lines of Seth and Cain in Chapters 4 and 5. But this would neglect the dimension of what were likely numerous other children had by Adam and Eve (5:4), and it is also questionable as to why the lines of Seth and Cain specifically, and not other human lines, would produce "mighty men".
2. It is noted that the phrase can have a "genitive quality" and be read as, "godly sons". But one wonders whether this would achieve a coherent parallel with the phrase "daughters of men," and there is also no particular reason why godliness ought to produce "mighty men" particularly when other human lines apparently do not.
3. It is said to resonate with that Israelis are called "children of God". Yet this is not the same as "sons of God", and one may ask: Were there no "daughters of God" marrying "sons of men"?
4. There is no evidence that the family lines of Cain and Seth were told to separate themselves from each other; there is no reason to consider the whole line of Cain as somehow "ungodly"; and there is no reason to suppose that the line of Seth was especially "godly". Indeed, was it godly to marry the daughters of men, if it was known they were generally wicked?

Both the fallen angels view and the line of Seth view have significant historical and textual support in Christianity, though the fallen angels view strongly coheres with the Ancient Near Eastern context and certain New Testament references.