The legal history of the concept of citizenship in the United States is remarkably circuitous. The original text of the constitution referred only to citizens of individual states, never to citizens of the United States. Consequently, federal law and jurisprudence lacked any conception of national citizenship until the decision of
Dred Scott v. Sanford in 1856, in which Chief Justice Roger B. Taney created the concept from whole cloth for the purpose of declaring Scott, a slave, not to be an American citizen and therefore not entitled to petition a federal court. The precedent held until the constitutional amendments of Reconstruction rectified it, explicitly introducing the concept of national citizenship into the constitution as a side effect.
There has remained a great deal of ambiguity about who is entitled to American citizenship by birth. Although the constitution as amended grants certain rights only to national citizens, the amendments that made national citizenship a part of the constitution failed to describe comprehensively who is entitled to citizenship. As a consequence, the question of who is and who is not a citizen, rather than being been decided on constitutional grounds, has been left to Congress. The odd result is that ordinary federal law, not the constitution itself, decides who is entitled to many fundamental constitutional rights and protections, including the basic rights to live in the United States and vote in national elections.
An interesting series of changes to the federal laws governing national citizenship occurred in the years after World War II. Because thousands of American soldiers and sailors were for the first time being permanently stationed abroad, there arose the question of whether their children born abroad had a right to citizenship. Federal law had previously granted citizenship to all children of American citizens, but during this period the laws were re-written to exclude the illegitimate children of military men with foreign women from citizenship in most cases. Today the law deciding the citizenship of children born abroad to a single American parent is a tangle of considerations of the marital status of the parents, when the child first visits American territory, how long he or she stays, etc.
I've sometimes wondered what the world might have been like in another several generations if those exclusions hadn't been made; by that time, due to the wonders of sexual reproduction, it's likely that tens or hundreds of millions of people outside the United States would be able to find an American in their ancestry, and therefore to claim American citizenship. Eventually, almost everyone would be an American. What would the world be like if everyone were entitled to vote in American elections (and obligated to pay American taxes)?