Depending on who you ask, "slavery" can be construed anything from the normal condition that "they" impose on "us" until such time as "we" can turn the tables and impose it on "them," to a ridiculous (or, depending on your point of view, insulting) dredging up of a discredited institution in a never-ending search for victimhood in an effort to control others through guilt.
The reality of slavery is probably properly located outside the parameters established by such creative victimology and its rejection by thoughtful people. The essence of slavery is not the control imposed on some by others (although that is slavery's most obvious characteristic), but the "condition of dependency" and the consequent deprivation of rights, whether tacit or explicit — a condition of being "wholly subject to the will of another; one who has no freedom of action, but whose person and services are wholly under the control of another." ("Slavery," Black's Law Dictionary.)
This is not to say that all conditions of dependency constitute slavery, or that all slavery is illegitimate. Children are "wholly subject" to the will of their parents until emancipation — although a wise or practical parent will allow greater freedom of action as a child matures as part of the training to become a functioning member of society. (The analogy between slaves and children in this context is so close that the Law of the Twelve Tables considered slaves and children legally equivalent, virtually the only difference being that children could expect emancipation on reaching majority, while slaves might be manumitted as a gift or as the result of self-purchase — but, fortunately, we don't need to get into that discussion, other than to note that, despite the "legal equivalence," even the Romans considered slaves and children as distinct.)
The case of "legitimate slavery" is even more controversial than the analogy between children and slaves. Nevertheless, legitimate slavery exists in the United States, as clearly stated in the Constitution. The Thirteenth Amendment abolished chattel slavery, that is, the power to own human beings as private property. It did not take away the right or responsibility of the State to control absolutely the actions of convicted criminals: "Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction." [Emphasis added.]
Under Roman law — which was the basis for the institution of chattel slavery as it existed in the United States and the justification for depriving convicted criminals of the exercise of their rights — the slave was considered as fully human as the free man. (Note that this discussion is within a legal context. It does not necessarily reflect individual or even group attitudes towards or beliefs about slavery, slaves, former slaves, or the descendents of slaves.) The only legal difference between a slave and a free man under Roman law was the fact of slavery that (again, under the theory in Roman law, not necessarily people's beliefs or actions) was imposed as punishment for a crime — not by nature, as Aristotle and the Greeks believed.
We see this in the different terminology used in Roman law. Today, "emancipation" and "manumission" have the same legal definition: "The act by which one who was unfree, or under the power and control of another, is rendered free, or set at liberty and made his own master" (or words to that effect). In Roman law, however, a child was emancipated, while a slave was manumitted. The sense in the former was that someone has a right to be free, and emancipation recognizes this right, while in the latter someone who does not have the right to be free receives it as a gift, and is recognized as free by manumission. This may be why Abraham Lincoln called his document the "Emancipation Proclamation" instead of the "Manumission Proclamation." The latter term would tacitly have acknowledged that the people being freed had been legitimately held as slaves. On the contrary — they had been enslaved illegitimately, and the language in the Emancipation Proclamation and the Thirteenth Amendment was phrased to reflect that fact.
Do the Emancipation Proclamation and the Thirteenth Amendment, however, mean that — except for convicted criminals — slavery no longer legally exists in the United States or anywhere else in the world?
By no means. Setting aside instances of chattel slavery being tolerated even though technically outlawed (vide Dr. Kevin Bales, Disposable People: New Slavery in the Global Economy. Berkeley, California: University of California Press, 2004), slavery in other forms is pervasive throughout the world, even among people who are convinced that they are free ("Slavery holds many men fast, but many more hold fast to slavery" — Seneca). There is, of course, slavery to sin and to unrestrained human urges, such as for food, drugs, and alcohol, but we're not concerned with that, either (at least, not in this discussion).
No, that with which we are concerned is economic slavery. This is a much more insidious, "hidden" slavery than the forms chronicled so well by Dr. Bales, although he covers even that in great depth when it takes the form of debt slavery or people being sold into prostitution.
In today's global economy, the most widespread form of slavery is the condition of utter dependency imposed on people by their reliance on the wage and welfare system as their sole or primary source of income.