Contemporary commentary I have read indicates that the phrase was intended to reach the children of anyone who did not fall within the complete and unitary "jusrisdiction thereof", in other words, no competing jusisdiction existed.
This encompassed many classes of individuals beyond those described.
"This encompassed many classes of individuals beyond those described."
But several SCOTUS rulings cited on this thread disagree, or at least disagree with the claim that Obama is not a citizen on the basis of his father's citizenship status alone. We can argue that a SCOTUS ruling was wrong or misguided, but we cannot arbitrarily wave them away. Perhaps, had I been on the SCOTUS for Wong Kim Ark I would have agreed with the dissenting minority, or perhaps not. I know for sure that I would have been on the other side of Roe v. Wade. That doesn't and won't change the law of the land.
Maybe there should be a law - or better yet, a Constitutional Amendment, since such a law would likely not survive a Constitutional challenge - to define in no uncertain terms who is eligible to be President, since the definition we have now has apparently lost clarity.