  Unlike classical correlation, quantum entanglement cannot be freely shared
among many parties. This restricted shareability of entanglement among
multi-party systems is known as monogamy of entanglement, which is one of the
most fundamental properties of entanglement. Here, we summarize recent
theoretical progress in the field of monogamy of entanglement. We firstly
review the standard CKW-type monogamy inequalities in terms of various
entanglement measures. In particular, the squashed entanglement and one-way
distillable entanglement are monogamous for arbitrary dimensional systems. We
then introduce some generalized version of monogamy inequalities which extend
and sharpen the traditional ones. We also consider the dual polygamy
inequalities for multi-party systems. Moreover, we present two new definitions
to define monogamy of entanglement. Finally, some challenges and future
directions for monogamy of entanglement are highlighted.
