The Bill of Rights, as the name implies, lists a wide variety of privileges of citizenship that cannot be taken from Americans without due process. You have the right to free speech, you have the right to bear arms, you have the right to a fair trial, etc. The right to vote, however, isn't mentioned.
In fact, though the Constitution offers some relatively detailed instructions on voting for president through the Electoral College, the document has far less to say about the right of Americans to cast a ballot in their own democracy. There are amendments extending voting rights to freed slaves, women, and 18-year-olds, and poll taxes are prohibited, but there's no additional clarity in the text about Americans' franchise.
Up until fairly recently, that wasn't considered much of a problem -- at least since the Jim Crow era, there was no systemic national campaign underway to undermine voting rights. But in the Obama era, the Republican campaign to suppress the vote has included restrictions without modern precedent, which in turn has started a new conversation about changing the Constitution to guarantee what is arguably the most fundamental of all democratic rights.
When the constitution was enacted it did not include a right to vote for the simple reason that the Founders didn't think most people should vote. Voting laws, at the time, mostly favored white, male property-holders, and the rules varied sharply from state to state. But over the first half of the nineteenth century, the idea of popular democracy took root across the land. Property qualifications were universally abolished, and the franchise became the key marker of white male political equality. Subsequent activists sought to further expand the franchise, by barring discrimination on the basis of race (the 15th Amendment) and gender (the 19th) — establishing the norm that all citizens should have the right to vote.
But this norm is just a norm. There is no actual constitutional provision stating that all citizens have the right to vote, only that voting rights cannot be dispensed on the basis of race or gender discrimination. A law requiring you to cut your hair short before voting, or dye it blue, or say "pretty please let me vote," all might pass muster. And so might a voter ID requirement.
The legality of these kinds of laws hinge on whether they violate the Constitution's protections against race and gender discrimination, not on whether they prevent citizens from voting. As Harvard Law professor Lani Guinier has written, this "leaves one of the fundamental elements of democratic citizenship tethered to the whims of local officials."
All of which leads to the question about a constitutional amendment, making the affirmative right of an adult American citizen to cast a ballot explicit within our constitutional system.