[DiogenesLamp]

What exactly are the citizenship rules/law for children born overseas of an American mother or father, or both?

The current situation is either an American mother or an American father can impart citizenship to a child born abroad provided they have spent a sufficient time (five years I think) after their 14th birthday in the United States.

This was not always the case. Prior to the Cable act of 1922, only fathers could impart citizenship to children born abroad.

[Nero Germanicus]

DiogenesLamp is correct. Here’s the section of current law on who qualifies as a “Citizen of the United States At Birth,” if born abroad:
“a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years”—8 U.S.C. § 1401

[gleeaikin]

If what you say is true, then I don’t know what all the fuss about Obama’s citizenship is except people not liking him or his views.