The powerful correlations known as quantum entanglement are responsible for many of the most interesting effects in quantum information and complexity theory, but remarkable as the correlations are, they are very tightly constrained. Most importantly, entanglement is monogamous: more entanglement between Alice and Bob means less between Alice and Eve. I will give an overview of some of the more useful mathematical manifestations of this law, from inequalities for entanglement measures, to the non-existence of symmetric extensions.
Laws of nature, unlike the laws of nations, cannot be broken. They can, however, be evaded. While entanglement cannot be created without some type of quantum mechanical interaction, it can sometimes be stolen in such a way that no one would ever notice. The phenomenon, known as "embezzlement" is alternately vexing and helpful, but aspiring quantum complexity theorists should be aware of it either way!