The Fourteenth Amendment changed the status quo. Specifically, the Amendment applied to the States. Section 1 of the Amendment reads:
“All persons born or naturalized in the United States and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.”
Upon initial reading, it would seem the privileges or immunities clause would be the most helpful in applying the Bill of Rights to the States. However, in the Slaughterhouse Cases, the Supreme Court severely limited the clause, to the point it has essentially, but not completely, been ignored.
While the privileges or immunities clause could have incorporated the entire Bill of Rights in one fell swoop, the Slaughterhouse Cases and other reasons for reluctance resulted in a piecemeal process through the Due Process clause.
Currently only the First, Second, and Fourth Amendment have been fully incorporated and held against the States. Only the Third Amendment, relating to quartering of soldiers, has not been held against the States in any regard. The remainder of the Bill of Rights has some clauses included with others excluded. A good outline of these various cases can be found here.
The most recent case addressing incorporation was in 2010, the Second Amendment case of McDonald v. Chicago. Now, American Citizens are protected not just from the Federal Government through the Bill of Rights, but also from the States thanks to the Fourteenth Amendment and the Supreme Court.