Quest for the Nephilim

There are both natural and supernatural interpretations of Gen 6:1-4. My preferred interpretation is that it alludes to conquerors and legendary warriors like Nimrod who found empires and dynasties. 

The standard supernatural interpretation views this as miscegenation between fallen angels and women. That, in turn, is sometimes viewed as a domestication of pagan tales about gods siring demigods by women. 

In modern times, we predictably have ufological interpretations of Gen 6:1-4 as well. I suppose that's a natural interpretation, inasmuch as extraterrestrials (if they exist) would be physical creatures. 

Although I've indicated my exegetical preference, suppose we consider a supernatural alternative for the sake of argument. Typically, the competing interpretations involve two kinds of beings: humans and angels. That's in large part because the Bible only explicitly describes the existence of two kinds of rational creatures: humans and angels. 

However, the Bible is not an encyclopedia. It doesn't profess to record everything that exists. Indeed, the Bible is severely selective in what it records. The Bible does have some obscure references that are hard for a modern reader to pin down (e.g. Lev 17:7; Job 4:12-16; Ps 91:5; Isa 13:21; 34:14). It's possible that there are other kinds of rational creatures which Scripture doesn't have occasion to mention. 

In theory, it's possible that a supernatural interpretation of Gen 6:1-4 is true, but it alludes to something other than angels. The angelic interpretation is a forced option based on very restricted conceptual resources, but there may be more to choose from. Again, though, I raise that possibility for the sake of argument